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This is to certify that the
thesis entitled

INTERNATIONAL TRADE, LABOR MARKET STRUCTURE
AND THE ORGANIZATION OF PRODUCTION

presented by

NICHOLAS SLY

has been accepted towards fulfillment
of the requirements for the

PhD degree in Economics

 

 

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INTERNATIONAL TRADE, LABOR MARKET STRUCTURE, AND THE
ORGANIZATION OF PRODUCTION

Bv

Nicholas Sly

A DISSERTATION
Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Economics

2009

ABSTARCT

INTERNATIONAL TRADE, LABOR MARKET STRUCTURE, AND THE
ORGANIZATION OF PRODUCTION

Bv

Nicholas Sly

This dissertation examines microeconomic aspect of international trade flows in
a general equilibrium environment. The primary focus is on firm behaviors such as
technology choice, the decision to export, product scope, and extensive export margin.
The influences of structural features of the labor market often overlooked are
emphasized. These include worker heterogeneity, labor market mobility, and the
matching behavior of workers. Considering the manner in which firms engage domestic
and foreign product markets, as well as labor markets, provides new insights into the
nature of international trade.

The first chapter considers firm technology and export decisions in an
environment where labor market mobility is significant and costly. I find that Job and
Worker turnover have opposing marginal effects on firm behavior; high job turnover
deters firms from adopting the best available technologies, while high worker turnover
leads to a greater share of firms using the best production modes. As a result industries
with relatively high worker turnover exhibit larger export intensity, lower wage

inequality, and spread the gains from trade among a larger share of the workforce.

Chapter 2 demonstrates the importance of worker behavior in trade adjustment.
Heterogeneous workers from matches endogenously, each vying for the bestjobs and
best partners. As international markets become more integrated, workers recognize
that export opportunities become larger while domestic markets experience greater
competition from foreign firms. Both cause the labor market to reorganize as workers
seek out new matches in order to secure export opportunities or avoid unemployment.
The post-trade liberalization allocation of the labor market is shown to be more efficient
in terms of aggregate productivity. Furthermore, labor market adjustments result in
infra-marginal changes in firms, as all firms experience changes in productivity through
new management.

Chapter 3 focuses on the how cross-country differences in the degree of
heterogeneity in labor endowments and the size of factor endowments jointly describe
the pattern of world trade. The theory makes two key predictions. First, high levels of
dispersion in ability within labor endowments make the costs of sub-optimal matching
more severe in terms of aggregate productivity. Second, high levels of dispersion make
poor matching outcomes less likely to occur. These predictions are evaluated using
data about international technology differences and cross-country differences in
educational attainment. Dispersion is shown explain much of cross country differences
in total factor productivity. Furthermore, information about trade flows reveals that
accounting for the level of dispersion in labor endowments improves the ability of the
Heckscher-Ohlin-Vanek theorem to explain factor trade based on the endowment sizes

alone.

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

List of Tables ............................................................................................................ v

List of Figures ........................................................................................................... v1

Chapter 1

Labor Market Turnover, Firm Technology Choice and Trade Preferences _______________ 1
Introduction---- - - - ................................... 1
Model _ ....................................... 7
Equilibrium -- - 11
Open Economy -- . - ...................... 30
Conclusion -- -- - 36
Notes ....................................................... - ....... 37

Chapter 2

International Trade, Wages, and Unemployment with Endogenous Firm Scope ,,,,,, 41
Introduction 41
Model--- - ............................... . ------- 48
Equilibrium ........................................... - ..... 57
Trade __ .................. j - ......... 62
Conclusion .. ........................................................................... 73
Chapter 2-Appendix A ................................................................................. 74
Chapter 2-Appendix B ................................................................................. 76
Notes ............................................................................................................ 78

Chapter 3

HOV and the Distributions of Factor Endowments .................................................. 83
Introduction= ............................................. 83
Model... -- ...................................................................... 89
Allocation of Labor .............................................. -- ...... 95
Distribution of Labor ............................................................... 101
Data .......... ................................................ 106
Empirics ....................................................................................................... 109
Conclusion. ..................................... 117
Chapter 3-Data Appendix - .................................... 119
Notes ...... ...... ............................. 126

References ............................................................................................. 131

 

iv

LIST OF TABLES

 

Table A.1: STAN Industry Codes and Descriptions _ ,,,,,,,,,,,,,,,,,,,,,, 120
Table 3.1: Mean and Dispersion of Labor Endowments across Countries ............... 128
Table 3.2: Estimated Hicks—Neutral Technology Differences ................................... 129

Table 3.3: Impact of Dispersion and Average Ability on

 

 

 

 

Aggregate Productivity ................................ 129
Table 3.4: Productivity Differences imposing Identical Dispersion Measures

across Countries (=US) ...130
Table 3.5: Sign Tests of the HOV Prediction- - - - ................. 130
Table 3.6: Rank Tests of HOV Prediction ............................................. 130
Table 3.7: Regression Tests of the HOV Prediction ................................................. 130

LIST OF FIGURES

Figure 1.1: Equilibrium Allocation of Managers to Technologies ............................. 39
Figure 1.2: Effects of Labor Market Turnover on Technology Adoption. .................. 39

Figure 1.3: Equilibrium Technology Adoption with Correlation between Quit Rates

 

 

and Managerial Skill _ _ ,,,,,,,,,,, _ -- _ _ _______ 40
Figure 2.1: Firm Product Scope and Extensive Export Margin ................................. 80
Figure 2.2: Determination of Employed Managers and Task Assignments. .............. 80
Figure 2.3: Labor Market Equilibrium ....................................................................... 81
Figure 2.4: Effects of Trade Liberalization ............................................................... 81

Figure 2.5: Adjustments is Matching Outcomes within 3 Median
Matching Regime ...................... 82

 

vi

Chapterl
Labor Market Turnover, Firm Technology Choice,
and Trade Preferences1

ABSTRACT: Firms choose to adopt one of several available technologies
and hire managers who are heterogeneous with respect to skill. The 1a-
bor force of each firm changes over time because workers who quit must
be replaced, and because jobs destroyed by capital failure must be up-
dated. Job turnover and worker turnover are both costly. Because of
variation in turnover costs across technologies, differences in labor market
turnover rates have consequences for the rate at which certain technolo-
gies are adopted. Job and worker turnover have opposing marginal effects
on a firm’s choice of technology, highlighting the importance of relative
turnover rates, rather than just total levels. High job turnover limits
industry adjustment to trade and may lead to an anti-trade preference

among a large share of the skilled workforce.

1 Introduction

Many characteristics of a firm, such as productivity, factor payments, and export
status, result from its choice of technology. Since workers are employed to utilize
the firm’s chosen technology, the selection process cannot be free from labor market
influences. The focus here is how labor market turnover, meaning both worker and job
turnover, affects a firm’s choice to adopt one of several available technologies. With an
understanding of how individual firms respond to the costs of creating and continually
staffing jobs on their production lines, I will examine the impact industry specific
turnover rates have on equilibrium outcomes such as income distribution, market

concentration, aggregate productivity and prices. The importance of labor market

turnover on the behavior of firms also has consequences for industry adjustment to
trade liberalization, and trade preferences of workers.

While little is known about how turnover affects the organization of the firm,
several micro-data studies from the last two decades have demonstrated the nature
of turnover in labor markets. Davis, Haltiwanger and Schuh (1996), DHS from this
point forward, characterizes job turnover within US. manufacturing industries. They
find that in nearly all industries a remarkably large number of jobs are being created
and destroyed simultaneously. From 1973 to 1988, between 11% and 19% of the
workforce was reallocated across production locations.

Observed job flows are distinct from worker flows since workers often leave jobs
when the firm continues to offer an employment opportunity. Burgess, Lane, and
Stevens (2000), BLS, call the worker movements into and out of employment that are
in excess job turnover "churning" in the labor market. Using employer level data
to parse the contributions of worker versus job turnover they find "...a considerable
amount of labor reallocation, primarily due to churning." Even for surviving jobs the
supply side of the labor market is mobile, causing firms to have to recruit a sizable
portion of its labor force continually.

Besides the large magnitudes of job and worker turnover which pervade all in-
dustries, DHS and BLS also find significant variation in both turnover rates across
industries. So to the extent that firms respond to turnover costs, industrial orga-
nization can vary widely because of mobility in the labor market. In addition to
the individual features of job and worker turnover, the relationship between them
is important. While both job and worker turnover rates are on average large with
significant variation, they need not be related. The determinants of job turnover,
or demand side turnover, are not the same as the determinants of worker turnover,
reallocation from the supply side of the labor market. In fact BLS confirm that

churning rates have only a weak correlation with job turnover ratesg. These facts

suggest that worker and job turnover are distinct economic events to which firms will
respond independently.

Many firms that manufacture similar goods use different methods of production,
and hire different types of workforces. Doms, Dunne and Troske (1997) find that the
firms which use newer technologies employ larger management teams, more educated
or skilled workers, and pay higher wages. The systematic pattern of technology
choices and hiring decisions indicates that while firms within industries are heteroge-
neous, much of their differences are rooted in endogenous choices rather than random
differences. Firm technology choice is a key determinant of other organizational
choices and seems a goods place to begin to examine the consequences of labor mar-
ket turnover in product markets.

A strong relationship exists between international trade and productivity. Going
forward, firms which export are typically more productive and use better technologies,
Bernard and Jensen (1999). And going backward, trade causes productivity gains
at aggregate and individual plant levels. At the industry level productivity increases
through a reallocation of production toward the most efficient firms, Pavcik (2002),
and at the plant level through technology and skill upgrades, Fernandes (2007). There
is also mixed evidence for learning-by-exporting as a source of improved firm produc-
tivity, among others see Blalock and Gertlet (2004) and Clerides, Lach, and Tybout
(1998). Labor market turnover can play an important role in the trade and produc—
tivity story by restricting or enhancing each of these avenues for trade adjustment.
The amount of job and worker reallocation influence the share of firms which adopt
each technology initially, and the number of firms who update their technology after
trade liberalization.

Turnover influences firm behavior because creating and filling employment posi-
tions are costly activities. Here I assume jobs using better technologies are more

expensive to create. Firms in a skill intensive sector choose which technology to

adopt, thus what type of jobs to offer. The workforce of an individual firm con-
sists of a single manager with a particular skill and a measure of identical labor.
Managers use their skill to take advantage of better technologies to improve labor
efficiency. High skilled managers are better at implementing technologies during
production. Firm heterogeneity arises within industries both because of endogenous
technology choices and exogenous managerial skill differences.

Each period after production a fraction of jobs are destroyed by capital failure.
Regardless of how productive a technology is at some point it breaks down or becomes
obsolete. When firms update their production lines they must pay to create new jobs
using the adopted technology. In line with the findings in DHS, job destruction and
creation are persistent events; they are not temporary shutdowns or start-ups of
activity. Destroyed jobs require new investments before labor is able to generate
output. Even though a firm continues to offer certain jobs over time, its labor force
may need to be reconstituted when a fraction of all workers quit. They might quit
to have children, retire, or relocate when a spouse changes jobs. These components
of job and worker turnover are outside the control of the firm.

In the following period firms update their production lines according to their
chosen technology and fill open employment positions generating industry-wide job
and worker turnover. The role turnover plays is only to reallocate the labor force.
Labor productivity does not evolve with greater employment tenure and a technology
maintains constant productivity throughout the duration it is used. That is to say the
marginal productivity of a firm depends only on the technology chosen and the skill
in which it is employed; the incidence of labor turnover has no impact on marginal
productivity.

High job destruction rates mean that firms have little time to recover their invest-
ment in technology, causing fewer firms to offer jobs using better, but more expensive,

technologies. When worker quit rates are high firms expect to have to pay to recruit

workers more often. As a result more firms adopt better technologies to maximize
worker productivity during their relatively short tenure3. The opposite influences of
job and worker turnover is an important feature of the model. While total levels of
turnover imply certain costs and thus hiring decisions by firms, the relative levels of
worker and job turnover are key in determining the allocation of labor to firms using
different technologies.

Better technologies raise the productivity of labor, increasing the amount of rev-
enue from which managers can capture rents. The demand for high-skilled relative to
low-skilled managers is greater in industries where more firms adopt the best available
technologies. Higher demand for a particular skill group implies a larger rent that
managers receive from each unit produced. As a result, industries in which more
firms adopt the best technologies will exhibit greater wage (per unit) and total in-
come inequality. Considering the response of firms to turnover costs, industries with
relatively high worker turnover (low job turnover) have greater income inequality.

Labor market turnover rates have consequences for the trade preferences of skilled
workers in each industry. Trade costs exclude some firms and managers from par-
ticipating in international markets. A reduction in trade costs lowers the demand
for managers who are not skilled enough to use better technologies; as a result their
nominal wages fall. Turnover rates determine the share of managers who face poten-
tial losses by influencing the share of firms which adopt less productive technologies.
Firms pass along costs to consumers, so the pattern of job and worker turnover deter—
mines if nominal wage reductions equate to real wage losses. Anti-trade preferences
are more common among skilled workers, and more likely to occur, when total labor
turnover is low, but job turnover is relatively higher.

Much of the literature on technology adoption has focused on how firms will choose
a continuous degree of specialization in production. In Acemoglu, Antras, and Help-

man (2007) and Yang and Borland (1991) firms can raise productivity by spreading

the production process over many specialized intermediate suppliers in environments
with incomplete contracts and transaction costs. Becker and Murphy (1992) show
how coordination costs and the general knowledge available in the economy limit the
optimal degree of specialization. The analysis here is closely related to Manasse
and Turrini (2001) and Yeaple (2005). Managerial skill interacts with technology
to increase productivity, and following Yeaple firms make endogenous choices about
which technology to employ4.

The topics examined here are also related to a literature that investigates the
role of labor market turnover in open economies. Cufiat and Melitz (2006) show
how diflerences in labor market flexibility across countries can lead to a pattern of
comparative advantage based on turnover rates. Davidson et al. (1999) and Davidson
and Matusz (2005) show how comparative advantage and the pattern of trade is
related to turnover rates when there are frictions in the labor market. While these
previous papers have emphasized how labor market turnover influences the allocation
of resources across sectors, the focus here is how turnover rates affect the allocation
of resources within sectors.

Trade preferences, observed as votes or campaign contributions have been used
to test results from traditional trade theories.5 Magee et al. (2005) are the first to
examine the role of turnover in determining trade preferences. Using job turnover
rates as a proxy for labor market mobility the authors show that PAC contributions
are consistent with predictions from the Heckscher—Ohlin—Samuelson model, when
there is high job turnover, and the Ricardo—Viner model, when there is low job
turnover. I show here that both the relative levels, and total levels, of worker and
job turnover have important consequences for trade preferences because they impact
the size and allocation of welfare gains of freer trade.

The rest of the paper proceeds as follows: section 2 describes the model. Section 3

solves for the stationary equilibrium and discusses the effects of turnover on industry

characteristics. Section 4 demonstrates how relative turnover rates impact the gains
from trade, and trade preferences of workers employed in export industries. Section

5 concludes.

2 Model

2.1 Demand

Consumers have identical preferences for goods X and Y. Good Y is a homogeneous
low-skill good. The skill intensive good X is a composite of a continuum of available
varieties. Each consumer has Cobb—Douglas preferences over the goods X and Y and

CBS preferences for the varieties of X.

 

U = (1—8)1nY+;31nX,where (1)
X = /z(i)adij and0= 1 .
. l—a
0 l

Given these preferences consumers will spend a portion 73 of their income on
varieties of X. The elasticity of substitution between varieties of X is 0.6 As shown
by Dixit and Stiglitz (1977) the consumption of varieties of X can be modeled by
considering the composite good X that has a price equal to the index that is a

weighted average of the price of each variety,

1
N It?
PX: Mal—0dr . (2)
0

Let E represent total expenditure. Good Y is the taken as the numeraire so that

demand for good Y is given by
Y = (1 - AW (3)

and the demand for each variety of X is

<——><——>

2.2 Workers

Each country is endowed with two types of infinitely—lived workers: a mass L of
laborers and a mass M of managers. Laborers are identical and supply a unit
of time inelastically. Labor cannot take advantage of better technologies absent a
manager. Each laborer can produce a single unit of Y, or any variety of X, when not
working under a manager.

Managers supply a unit of time for production and are heterogeneous in their
skill level, given by s, for implementing technologies. The skill of each manager is
observable but exogenous to the hiring firm. Skill intensity in the X sector refers to
the ability of managers to use their skill to organize production in a way that improves
labor productivity. Managers in the X sector provide only supervising services. No
manager can improve labor productivity in the perfectly competitive Y sector, and
so works alone producing output according to her skill level. The distribution and
density of managerial skill are G (s) and 9(3), respectively, and have support (0,00) .

The markets for managers and laborers are perfectly competitive. Since laborers
have the same opportunities regardless of the sector in which they are employed, and
regardless of the technology adopted by their employer, labor wages will not vary
across individuals. Differences in managerial ability will lead to dispersion in skilled

wages.

2.3 Production

Firms are free to enter both industries. Entry consists of adopting a production
technology, and in the skilled sector hiring a workforce simultaneously. There is
only one available technology for good Y. If the firm enters the X industry then it
produces a unique variety using one of two available technologies: H, for "high-tech"
and L for "low-tech". The "high-tech" method of production can be thought of as a
greater division of the production process so that when manufacturing output, labor
benefits from specialization. Each firm in the X sector hires one manager and as
many laborers as needed.

Adopting the Y technology is costless. To create a job opening a firm must pay F L
per position when using technology L and F H per position when using technology H.
The natural assumption is F L < F H- All labor is qualified to use the Y technology
but there are costs, It, to recruiting and training labor to use either technology in '
skilled X sector. Job creation and recruiting costs are given in terms of output that
must be produced but cannot be sold, as is standard.

The productivity of labor within a firm in the high—skill sector depends on the skill
of the manager hired and the technology the firm adopts. Labor does not benefit
from using better technologies separate from the skills of a manager. In essence,
unsupervised labor uses technologies with a skill level 3 = 0. A manager using the L
or H technology can increase the productivity of any size of labor force, or work alone
employing her skill level, 3, using the Y technology. So, each worker using technology
j E {Y, L, H}, under the supervision of a manager with Skill 3, can produce fj(s)
units of output.

More skilled managers have comparative advantage in employing better technolo-
gies. When using the same technology, the labor force with the more skilled manager
is more productive; i.e. f, (s) is increasing and continuous in 5. When using dif-

ferent technologies with a manager of the same skill level, the labor force using the

better technology is more productive. The following two conditions summarize the

characteristics of the technologies.

 

 

 

fY(0) = fL(0)=fH(0)=1a and (5)
afH(S) 1 3fL(3) 1 aft/(8) 1
as Ms) > as me) as fy(s)>0

2.4 Turnover

Industry X faces two sources of labor market turnover that occur exogenously after
production: worker quits and job destruction. Workers leave employment positions
for various personal reasons that are unrelated to the wage paid by the firm. Here
workers do not quit to engage in rent seeking behavior7. Job destruction occurs due
to exogenous capital failure. Technologies wear out or become obsolete after some
time and must be replaced, however their productivity is constant until the point of
failure.

In a single interval of time jobs are destroyed with a constant probability 6. Cre-
ating new jobs entails opening new positions using the firm’s technology at a cost of
F, per position, and training new workers to employ the technology at a cost of it
per position. Some workers quit their jobs even when the firm continues to offer the
employment opportunity. When a fraction 7 of a firm’s labor force quits replacement
workers must be trained at a cost of k per worker.

The skill of the manager is constant and technologies maintain their productivity
regardless of job duration. Therefore, firm productivity is not aflected by the tenure
of the worker or age of the technology; the implication being that turnover does not
affect productivity at the margin. Applying the law of large numbers to each firm,
6 of all the jobs at a firm will be destroyed and y of the firm’s surviving jobs will

need to be restaffed when employees quit; of course when new jobs are created to

10

replace one where a worker simultaneously quit, the firm only has to pay to recruit
one worker. So the expected turnover costs to the firm that hires a manger of Skill

3 to use technology j, and hires the optimal size of labor force I (s, j), are
[5 (Fj + k) + 7k — 671:] ((8,3). (6)

There is no turnover in the Y industry. Though turnover in the Y industry
may exist the purpose here is to examine how turnover rates affect firm behavior
within a sector, holding the turnover rates of all other sectors constant. Firms in the
Y industry produce a homogeneous product with a costless technology, so they do
not face any chance of becoming obsolete or having to pay to replace capital. And
since labor market turnover is taken to be exogenous for any industry, it need not be

modeled explicitly in the Y industry.8

3 Equilibrium

I will focus on the derivation of a stationary equilibrium in a closed economy. In-
dustry Y is perfectly competitive in its production of the numeraire good. Hence the
marginal revenue in each period for a firm in the Y industry is constant and equals
1. Industry X is monopolistically competitive, giving rise to the well know revenue

function for a firm producing variety 2',
' = BEPU-l ' 1‘0 7
7‘0) , X 19(2) ( )

As is standard, these firms will charge a price equal to a fixed markup over per

unit costs. The markup is Z11" Define the per unit costs of producing with technology
j as 03- for j E {Y, L, H}. Under the supervision of a manger with skills 3, a labor

can produce fj(s) units of output. Labor is paid a wage v and managers are paid

11

W(s) by the firm. Thus the per unit cost of production satisfies 1(3, j) fj(3)Cj =
221 (s, j) + W(s); the total output of the the firm times the per unit costs equal total

production costs.

1

3. 1 Wages

Since good Y is the numeraire, and the productivity of labor without a manager is
one unit of output, a perfectly competitive market will result in a labor payment of
v = 1. Differences in skills result in differences in managerial opportunities which
lead to dispersion in skilled wages. The distribution of wages for skilled activities
depends on the allocation of managers across different technologies.

Free entry by firms and a perfectly competitive market for skilled activities ensure
two features of the skilled income distribution must hold: the skilled wage per unit
of output is constant and is increasing in the skill of the manager. Each laborer has
the same outside option regardless of the technology adopted by their employer, so
the surplus generated by increased labor productivity must be captured by either the
firm or the manager. With free entry in the X sector, fear of other firms poaching the
manager erodes the ability of the hiring firm to capture any of this surplus. Hence
the manager is paid the whole of the increase in each laborer’s productivity from
implementation of the firm’s technology. The manager applies her skills to the entire
labor force, extracting the same wage from each unit of output. Managerial wages
are increasing in skill because better managers generate more output.

Managers recognize that their wages depend crucially on the productivity of labor
under their supervision. Therefore every manager will prefer a job using the best
technology. Firms observe the distribution of managerial skill and will make its hiring
and technology choices optimally. Each firm will try to hire the manager with the
highest skills to manage its production lines. In the perfectly competitive manager

market the combination of managers looking for jobs using the best technology avail-

12

able, and firms trying to hire a manager with the most skill, leads to a equilibrium
where managers are positively assorted across technologies based on skill. For a
given manager with skill level 3, using technology j, there will be no other managers
with a skill level less than 3 using a more efficient technology than j in equilibrium.
The most skilled workers will find jobs managing a firm that uses the best available
technology. The least skilled workers will be self-employed in the Y sector.

As managers in the skill intensive sector capture the rents created when they
increase labor productivity, the firm’s average production costs do not change. Any
potential savings on labor wages are paid in full to the manager. Then any two
firms using the same technology have the same unit costs, regardless of the skill of
the manager hired. That is to say 0, = [(5,3) 12+ W(s)/l (s,j) fj(s) is constant over
s for all firms that use technology j. Unit costs vary across technologies H and L

because of the difference in returns to skill across technologies.

3.2 Allocation of Managers to Technologies

Define 81 as the most skilled manager working in the Y industry and 32 as the least
skilled manager employed by an H type firm in the X industry. A manager with
skill level S 1 is indifferent between the wages she earns in the Y sector or managing a
firm using the L technology. A manager with skill level 32 is indifferent between the
wages she earns using the L or H technology. Consistent with positive assortative
matching, all managers with skill less than or equal to 81 work in the Y sector and
all managers with a skill level above SQ use the H technology.

Firms which adopt the L technology will hire workers such that s E (31, SQ) if
they exist. Firms using the L technology will arise in equilibrium only if the fixed
cost savings relative to the best technology (CHFHI (s, H) -- C'LFLI (s, L)) are large
enough, and the demand for X is large enough. From this point forward I assume

the more interesting case where costs and the size of the market are such that L type

13

firms appear in equilibrium.
Rearranging the expression for unit costs, 03-, for each technology gives the skilled

wage distribution over skill, s,

fY(5)CYi 0 S s S 31
W(s) = [(3, L) [fL(s)CL — 1], 51 g S 5 $2 - (8)
[(3,H)[fH(S)CH—1j, 3235

Marginal revenue in the perfectly competitive Y industry is 1, and because the

cutoffs S 1 and 52 are defined such that the worker is indifferent between the wages

she earns using either technology, the unit costs can be written9

CY = I
_ fY(51)+1(S1,L)
CL _ ( 1(SlsLlfL(Sll )<1
[(SZ’L) fL(S2) (fY(Sl)+l(Sl,L)) + 1(SQ,H) _Z(SZIL)
l(52,11l)fH(32) 1(SiiL)fL(Sr) 1(52,H)fH(S2)

 

 

 

< CL (9)

These last two expressions completely describe the skilled wage distribution in
equilibrium given the allocation of managers to each technology. The two skill cutoffs
are obtained from equilibrium conditions in the Y and X industries. Specifically
the market clearing condition for Y and the free entry condition for firms in the X

industry.

3.2.1 Y Market Clearing Condition

The total demand for the low skill good is Y = (1 — [3) E. There is no saving in
the stationary equilibrium so total expenditure in the economy is equal to the sum of
total skilled wages and all labor earnings. Given the skilled wage distribution above

for the mass of workers M, and the mass of laborers L, total expenditure (E) in this

14

10

economy is
s, 32
f [fl/(8)] (16(3) + .I1(3 L) )(IfLS )CL -1l01G
E=M 0 00 51 +L
+5]. l(8,17)If1:r(8)CH —1ldG(8)
2
S1
gfy YS(S)()dG +‘:f2(SCLl LSS+)fL()dG()
= [If 00 + L (10)

ofOCHH (3 H) fH /l(3,-)

52 0

Now, the total payments to workers in the Y industry is the sum of skilled and labor
3, 0°

wages: A! f fy(::)dG(z) + L — /l (3, -)dG (3). When the Y market clears, total
0

0
expenditure on good Y equals total payments to workers in the industry, or

(1TB)51— fffls) )dG(s )+/1(8,-)d0(3)+filf_f}=

I

52 00
f I (s. L) f. (s) dG(s> + $5; / z (s. H) fH<s>dG<s> (11)
S1 5‘2

3.2.2 Free Entry Condition in X Sector

The second equilibrium condition is derived from the free entry conditions for L and
H type firms. The value of entry into the X industry is equal to the stream of
expected profits earned from entry, less sunk entry costs. The probability of job

survival is (1 — (5) and the probability of having to replace a worker for a surviving

15

job is '7'. Hence,

Ve(3) = —C',- [173+ 13] l(3,j) +
00
mJax/exp(—pt) (rj - l (3,3) — W(3) — C'j { [6 (F, + k) + 7k — 67k] l(3,j)}) dt
0
At low levels of discounting the fixed barrier to entry is uninhibiting, leading firms
to earn zero profits in equilibrium. For monopolistically competitive firms the zero

profit condition takes the following form, where revenues are a constant mark-up

expected turnover costs:
rj 2003- [6 (Fj +1.3) +yk—67k] [(3,3) (12)

The relationships between output and revenue for any two firms with H and L tech—

nologies are functions solely of their unit costs. As can be derived from (4) and

(7), 1
33H CH _0 TH CH _,,
_ = _. — = —— l.
55L (CL) and (CL) ( 3)

Then combining (12) and (13) yields

(14)

 

:11 =(€&)1—0 = CH I5 (Fj +13) +719 - 57k] l(siH)
r1. CL CL [6 (F,- + k) + 7k .- 5719] 1(3, L)

The free entry condition for both L and H type firms is fulfilled by skill cutoffs that

meet the condition above, or

 

0—H = ([6(FH+k)+7k—67k]1(Sg,H));01' (15)
CL — [5(FL+k)+’7k—d7k]l(32,L)

16

3.2.3 Equilibrium Allocation of Managers to Technologies

An equilibrium allocation of managers to technologies occurs when both the Y market
clearing condition and free entry condition are satisfied. Thus the equilibrium values
of $1 and 52 occur at the intersection of equations (11) and (15); these conditions
are illustrated in Figure 1.1. The opposing slopes of the two conditions guarantee
that the equilibrium is unique.

Total differentiation of the market clearing condition for Y shows that 51% < 0.
The requisite skills needed to obtain a management job at a high tech firm is inversely
related to the necessary skill level to find a job at any firm in the X industry. The
inverse relationship between the skill cutoffs has an intuitive justification. As more
firms adopt the best technology (52 falls) average labor productivity rises in the skill
intensive sector, increasing total income. When income rises so does spending on
good Y, which increases the demand for the low skill good (8'1 rises).

The free entry condition is upward sloping; 3% > 0. When the value of 31 is
low there are many firms operating in the X sector. With a large amount of variety
for consumers and greater competition in the market firms can only justify entry if
they can capture enough market share. Adopting the best technology makes a firm’s
particular variety relatively less expensive to produce and able to be sold at a low
price. Hence a low value of 31 must be associated with relatively greater number of

firms using the best technology; i.e. low value of SQ.

3.3 Turnover Effects

3.3.1 Turnover & Allocation of Managers

Now we can address specifically the questions of this analysis: how is firm behavior
regarding technology choice affected by labor market turnover rates? Notice that the

free entry condition in (15) is a function of the labor market turnover rates 7 and 6,

17

while the Y market clearing condition is not. The equilibrium allocation of managers

responds to turnover costs via the entry channel only. Differentiating we obtain

q

56ft) 1 (5(F +k)+ks—57k L3—
66L =(FL‘FH)(E) (6(F;+k)+k7—67k)
X ( 7k1(32,H)1(32,L) )2) <0

(6(FH +k) + k7 — 67k

q

E 6(FH+k)+k7—67k

X ( 6ki(32,H)z(32,L) ) > 0

(6 (PH + k) + k7 — 67102

An increase in job turnover rates shifts the entry condition downward, raising the
skill requirement for being hired to manage the best technology. (95:2 > 0). In
industries where job turnover is more likely, the expected stream of income coming
from a job using either technology is shortened, giving firms less time to recover their
sunk investment costs. Only the most skilled managers increase labor productivity
enough to justify the expense of the H technology.

Worker turnover rates have the opposite effect of reducing the skill requirement of
the best technology ($3 < 0). Industries with higher worker turnover rates have
higher expected future costs of using either technology because firms will have to pay
to recruit workers more often. As a result more labor will be allocated to the H
technology.

Worker and job turnover rates have opposite effects on the adoption of technologies
specifically because of how they affect the relative shares of worker and job turnover

costs, as compared to the firm’s total turnover costs, associated with using each

18

technology. The right hand side of (15) is the ratio of the expected total turnover costs
for firms using the H and L technologies. Higher expected turnover entails higher
costs of using any technology. But since creating an H type job is more expensive,
higher job turnover rates make the H technology relatively less appealing. On the
other hand, firms using either technology face the same expected worker turnover
costs per position. When worker turnover costs are higher, the relative difference in
costs between H and L technologies is smaller. At high levels of worker turnover
both technologies become more similar in terms of total turnover costs, inducing a
larger portion of firms to choose the lower unit cost (H) technology.

There does not seem to be any comprehensive empirical assessment of the rela-
tive size of these costs. Richer models of the costs associated with job and worker
turnover might yield different or more interesting results. However regardless of the
specification of turnover costs across technologies and workers the key determinant
is the relative cost shares of worker turnover and job turnover associated with either
technology. As we will see, the relative cost shares of labor market turnover have
far reaching consequences for wages, industry productivity, market concentration and
trade adjustment.

For the rest of this article I will use the response of the equilibrium cutoff values
S1 and 52 to describe how labor market turnover shapes the equilibrium. Using
the fact that the Y market clearing condition is upward sloping, each turnover rate
has the opposite effect on the allocation of managers between sectors: d—dsal < 0 and
5%- > 0. The first proposition summarizes the relationship between the turnover
rates and the equilibrium allocation of managers to technologies. The results are

illustrated in Figure 1.2.

Preposition 1 A higher job turnover rates raises 32 and reduces 81. A higher

worker turnover rate decreases 5'2 and raises 5'1.

19

3.3.2 Turnover & Firms in the Skill Intensive Sector

Average productivity and the distribution of sales across firms in the X industry
depend on the relative number of firms that adopt each technology. The total
number of firms in the X industry determines product variety, and average sales
concentration. Together the total number of firms and relative number using each
technology determine aggregate prices. From the fact that the equilibrium cutoffs 51
and 32 are inversely related we know that as more firms adopt the best technology,
fewer firms enter using the second best technologies, and visa versa. Proposition 1
shows how the relative adoption of each technology depends on labor market turnover
rates. So to describe response of product variety, sales concentration and prices to
turnover, what remains to be demonstrated is how the total mass of firms using each
technology depends on expected turnover costs.

The market clearing conditions for both L and H type varieties establish how
many firms adopt either technology in the skill intensive sector. In a stationary
equilibrium the number of firms is constant over time. Total production in a single
time period by H type firms is M {ff}; (3)1 (3,H)dG(3). Output by firms using
the H technology either goes to coffgr job creation costs, worker recruitment costs,
or to market. A fraction 6 of active jobs are destroyed every period and the same
number of jobs are created in the next period at a cost of F H units of output per
position. Each new job created by a firm using the H technology must be filled by
a new worker. Employment positions within the firm may survive, though the firm
will have to replace any workers who quit. Each worker that must be recruited costs
the firm It units of output. The remaining output of the firm is sold to consumers.
Using X’] and [(7’) to denote respectively the output and number of workers employed

by a representative firm using technology j, the market clearing condition for H type

20

varieties is

NH (3%}; + [6 (FH + k) + k») —— 67ch 1777)) = M ] fH(s)l (3, H) (10(3) (16)
52

By similar construction for L type firms, and using the fact that

X;- = (o — 1) ({6 (Fj + k) + ky — 67k} (TD), we can write

NH = A1 ~ /fH(3)l(3,H)dG(3), and (17)
o ([5 (FH + k) + is) — 67k] 1 (111))52

 

M
0([6(FH+k)+k7—6yk

 

32
N ~ f (s)l(s,L)dG(s).
L W16)! L

N, is the total number of firms which adopt technology 3' in equilibrium. The
first term in the equations in (17) reflects the labor market turnover costs expected
upon entry. As is natural, higher turnover costs lead to less entry of firms using any
technology. The second term on the right hand side of equations (17) indicate the
relative adoption of each technology.

As more firms adopt the best technology the distribution of sales becomes more
skewed towards the largest firms in the industry. This happens first because as
more managers and labor begin using better technologies, they become more efficient
during production. The productivity gain to these workers from a better technology
is reflected in the price charged by the firm. A lower price allows firm which adopt
the H technology to increase market share. Furthermore as more firms adopt the
best technology total income rises. Large firms, that employ the best technology
initially, can expand production as other firms upgrade their technology because of
increased demand. Both reallocations imply larger market shares held by the largest

firm in an industry.

21

Total labor market turnover costs are important determinants of the average sales
concentration among firms by limiting market participation. But the relative costs of
worker and job turnover affect how the distribution is skewed toward firms using either
technology. Then turning to the role turnover plays in firm entry, and on technology

choices from proposition 1, the following results are obtained.

Proposition 2 The average sales concentration is increasing in both the job turnover
and worker turnover rates of an industry. Industries with higher job turnover ( larger
6 ) will have a less skewed distribution of sales across firms. Industries with higher

worker turnover ( larger 7) have a more skewed distribution of sales across firms.

Given the differences in the productivity of labor using each technology, changes in
the proportion of firms which adopt either technology have implications for aggregate
industry productivity. Adoption of the H and L technologies by firms are inversely
related so an increase in the share of firms which adopt the best technology necessarily
raises average productivity in the industry. Using the response of firms to labor
market turnover, average productivity depends on turnover rates in the following

way.

Proposition 3 Average labor productivity is higher {lower} in industries with rela-
tively higher worker { job ) turnover, and is lower in industries with higher levels of

total labor market turnover.

Turnover is costly and so hinders firm productivity. However, higher worker
turnover could possibly result in greater average productivity. Though there is no
advantage to worker-firm separation embedded in the model the allocation of man—
agers to technologies is improved with relatively high mobility in the supply side of
the labor market. Job turnover always has negative effects of average productivity

since it is costly and discourages firms from adopting better technologies.

22

3.3.3 Turnover & the Income Distribution

Each laborer makes the same wage regardless of the technology he is using. Managers
capture the surplus created by increased labor productivity which varies across skill
level and technology used. Technological adoption has already been shown to depend
on labor market turnover rates. This section explores how firm responses to turnover
rates influences the income distribution.

The perfectly competitive market for skills ensures that every manager using a
particular technology earns the same wage per unit of output. Then besides the direct
effect of changing the allocation of managers to technologies, turnover rates have an
indirect effect on the skilled wage distribution by influencing the per unit skilled wage.
Even the wages of those managers who use the same technology at various levels of
job and worker turnover will respond to changes in technological adoption. Managers
supply their services inelastically but the rate at which each technology is used affects
the relative demand for certain skill levels.

Combining the two components of the skilled wage distribution in (8) and (9)
gives the income distribution as a function of a particular manager’s skill level, and

the equilibrium skill cutoff values.

 

 

fY(S). 0 < S S SI
fY(Sl)+l(Sl,L) _
W(3) = l(s, L) [rL(s)( «51.1» ms}, ) 1], S, S , S S,
l(1‘32»L)J’1.(52) fy(31)+l(Sl,L)
[(8111) fH(8)z(S2.H)fH(32) ( I(Sl,L)fL(Sl) ) 82 S S

l(32,H)-l(52.L) _ 1 ’

 

T 1(stHlfH(S2) ( )
18

In order to fully characterize the effects of labor market turnover on income
distribution there are five different classes of skills to consider: those who remain

employed as managers by each of the three firm types regardless of turnover rates, and

23

those near each cutoff skill level that get sorted into managing a different technology
for various turnover rates. As the two equilibrium cutoffs adjust managers with skills
near the cutoffs will have the most severe changes in income; the technology she uses
changes and the return to her skill using that technology changes. Since 31 and 82
always move in opposite directions we can discuss the each type of turnover more
conveniently in terms of the number of managers who will find employment at L type
firms. Job and worker turnover either increase or decrease the size of this "middle
class".

High worker turnover results in a smaller "middle class". ((175,);2 < 0 and thus
6%- > 0.) Workers at the upper fringe of the middle class for low worker turnover
rates can find work at H type firms, where they earn higher wages, when worker
turnover rates are higher. Subsequently, the lower fringe of the middle class is
allocated to the low skill sector at higher worker turnover rates, resulting in lower
income. Worker turnover benefits the top of the skill distribution at the expense of
low skilled managers.

Now consider the workers who obtain jobs managing a labor force using the same
technology for various levels of job and worker turnover. The price of the low skill
good Y is taken as the numeraire so income from that sector fixed and equal the
manager’s total output when self-employed. Now consider skilled wages of those
who are employed by L type firms for any level of job/ worker turnover, the perennial
middle class. The premium paid per unit of output at L type firms is decreasing in
skill requirement for managing the L technology.

In an industry with relatively high worker turnover. The resulting high value of
31 and the associated low value of 5'2 mean that fewer firms demand managers with
moderate skills. The lower demand results in a lower skilled wage per unit. In a
similar manner, the premium paid to managers at firms that adopt the H technology

is decreasing in SQ. As more firms adopt the best technology in response to high

24

worker turnover, demand for the highest skills increases, raising the premium paid
per unit of output to the highest skilled managers.

All together the impact of firm technology choices on the skilled income distri—
bution and results in proposition 1 make clear predictions about how labor market

turnover affects income inequality“.

Proposition 4 Industries with relatively higher worker turnover exhibit greater in-
come inequality across skill. Industries with relatively higher job turnover exhibit less

income inequality across skill.

The last proposition demonstrates how the distribution of nominal income is in-
fluenced by the relative levels of job and worker turnover. However the impact of
worker turnover on real income cannot be described in general. A larger share of
people using the more advanced H technology raises total productivity and thus total
income. However if greater adoption of the best technology results from relatively
higher worker turnover costs, then it is not clear if real income increases. Presumably
higher turnover costs get transferred to consumers via aggregate prices. The next
section explores the relationship between labor market turnover has with welfare and

prices.

3.3.4 Turnover & Welfare and Prices

The ambiguous effect of total worker turnover rates on real income also means that
the effect on social welfare is ambiguous. Turnover in this model is solely a cost
burden to the economy. A social planner would prefer to let the initial efficient
allocation of managers across technologies and labor hiring decisions be maintained.
So the statement above that the effect of worker turnover is ambiguous should be
interpreted that one cannot say in general whether a higher level of worker turnover
raises welfare; what is clear is that at the same level of total turnover costs, a relatively

large share of turnover costs coming from worker turnover is more favorable.

25

Real wages depend both on income and prices. So far I have shown how nominal
wages, that is wages in terms of the price of Y, are related to labor market turnover.
The aggregate price index for the X industry can shed light on the labor market
conditions under which real wage gains and welfare gains are most likely. Every firm

in the skill intensive sector charges the same markup over unit costs, so from equation

(2)

PX: )1/1—0'.

QIH

( YHC‘}{_U+NLC}J-o

Substituting for the equilibrium number of firms from (17) and simplifying using the

market clearing condition for Y the price index of X can be written.

N 1
1{a(1—,s)[5(FH+k)+ks —5s,k]i(L)}U_—T
PX—g

 

,3M
31 00 1—1-_a
X CEO /l(3,Y)fy(s)dG(s) +/l(-s:)dG (s) — 1
0 0

The first term in braces is increasing in both turnover probabilities. This is the
"level effect" of higher turnover. Firms pass these costs along to consumers. The
second term in braces is decreasing in SI. Thus it is the case that the efficiency
gains from greater use of the best technology outweigh the losses in variety. This
is the "share effect" of relatively higher turnover costs from either job or worker
reallocations. Since 31 increases with the amount of worker turnover, the share effect
is positive for total welfare. High job turnover rates necessarily increases prices since
fewer high-tech firms will operate in equilibrium. Thus relatively higher worker
turnover rates may induce price savings if total turnover is low, but job turnover

always causes prices to rise.

26

3.4 Worker Quits and Skill

So far the assumptions about the costs associated with labor market turnover have
been that high-tech jobs are more expensive to create than low-tech jobs, and that
all workers are equally likely to quit their jobs. Even though worker turnover is
exogenous we can examine other models of worker quits that may be more empirically
relevant or intuitively satisfying. In this section I assume that labor working for less
skilled managers are more likely to quit. Specifically, a firm that hires a manager
of skill level 3 faces the probability 7 (3) that each laborer will quit his job before
the next period, where 7’ (s) < 0. Thus in addition to being less productive when
working under a less skilled manager, labor quits cause turnover costs to be higher
at firms which hire low skilled managers.

Note that since managers capture all of the surplus from increased productivity,
quits by laborers working under low skilled managers cannot be interpreted as rent
seeking behavior. Labor earns the same wage regardleSs of productivity. Even so,
there is at least anecdotal evidence that labor is less likely to quit when worker for
better management. This section provides an examination of how robust the previous
results are to various models of job and worker turnover.

Compared to the previous discussion, correlation in worker quit rates and manage-
rial skill affects the ear-ante entry and hiring decisions by firms because the expected
turnover costs per position will depend on the skill of the manager that is hired,
not just the technology adopted. The equilibrium conditions used before need to
be modified slightly to account for the relationship between skill and probability of
worker quits. Still assuming that market size and fixed costs are such that in equilib-
rium there are firms who choose to adopt less productive technologies, equation (15)

becomes

 

gfl : ([6(FH+k)+k(1—5>r(32)ll(Sg,Hi)%1
CL _ [6(FL+h)'I—k(1—6)r)/(82)]Z(SQ,L)

27

Relative to the case with no correlation between skill and quits, the ratio of total
turnover costs between the H and L technologies decrease more sharply in skill. The
reason being that as skill rises, worker turnover falls, and so differences between
turnover costs between the H and L technologies become increasing dependant on
the differences in job creation costs, F j. As before, at low levels of worker turnover
the best technology appears relatively more expensive.

When making comparisons across industries based on labor market turnover with
correlated skill, the way that quit rates differ is important. A "high worker turnover"
industry could mean that at all skill levels quit rates are higher, or that quit rates
decrease slower with skill. To consider both cases suppose that the probability of
worker quits in a "high worker turnover" industry is affine transformation of 'y (s)
(quit rate in a "low worker turnover" industry) of the form a + by (3), where a > 0
and b 2 1.

Quit rates between the high and low turnover industries differ by the same absolute
amount for any level of managerial skill if b is held constant across industries but a
differs. Expected turnover costs for each technology in the high turnover industry are
shifted upward. But if the strength of the correlation between skill and worker quit
rates varies across industries, then the high turnover industry can be characterized
by a higher value of b. Differences in the correlation of skill and quit rates will cause
expected turnover costs for each technology to rotate around the point where 82 = 0.
This equilibrium condition and the impacts of higher worker turnover of both types
are depicted in Figure 1.3.

Regardless of the specification of high worker turnover in a particular industry,
the result is the same. Higher worker turnover reduces the requisite sill level for
using the best technology. High worker turnover reduces the relative cost differences
between the H and L technologies, causing more firms to adopt the best technology.

The previous results are robust to an inverse relationship between managerial skill

28

and quit rates.

3.5 Discussion

The model laid out above makes several assumptions about the interactions of tech-
nology, labor and managerial skill. Some are made for analytical convenience and
are not crucial to the results obtained. In this section I delineate which features of
the model can be generalized and which are necessary the results obtained.

First, the assumption that labor cannot take advantage of better technologies
absent a manager simply pins down outside opportunities of labor. If laborers could
take advantage of better technologies during their then the economy would require a
rationing rule for who is hired by firms using the best technologies. Since labor is
homogeneous an arbitrary rule would not affect firm technology choice at the margin.
The need for skilled oversight to take advantage of better technologies is not a crucial
feature of the model.

Next, skill intensity in the X sector describes the ability of managers to lend
their skills to labor working under their supervision. Restricting managers to be self—
employed in the Y sector guarantees that at least some managers seek employment in
the skilled sector. If there were no differences in skill intensity between sectors, then
all managers would seek employment in the perfectly competitive Y sector. In the
perfectly competitive Y sector managers capture rents from increased productivity
while facing a constant marginal revenue curve, rather than a decreasing one in the X
sector. Requiring self-employment in the low skill sector is a simplifying assumption
to guarantee that all technologies are adopted in equilibrium. However, the marginal
impact of labor market turnover on firm technology choice is not contingent on this
assumption.

Neither the partial interactions of labor and technology, nor labor and skills, have

an impact on the marginal behavior of firms regarding technology choice. Thus the

29

key feature of the model must be the interaction of managerial skills and technology.
The ability of more skilled workers to apply technologies more efficiently results in
the particular allocation of factors during production discussed above. I now turn to
the description of that allocation in a open economy and discuss how labor market
turnover rates influences industry adjustment to trade and trade preferences of skilled

workers.

4 Open Economy

Several studies have established the link between the export status and the produc-
tivity of a firm. Since a firm’s productivity is partially a result of its choice of
technology, we can extend that link to labor market turnover. The trading environ-
ment that I will consider here is between two identical countries so that wages are
equalized, and Y is not traded in equilibrium. Intraindustry trade in the X industry
occurs as consumers desire foreign varieties.

Potential exporters face variable iceberg transportation costs 7' and fixed exporting
costs F3; if they choose to serve foreign markets. For any optimally chosen size of

2

labor force1 assume the beachhead costs satisfy

Condition 1

[6(FH + k) + (1 — 5) 71.] r (3, H) > F1704 > [6(FL + k) + (1 — 5) 7k] 1 (s, L)

The implication is that only firms using the best technology export in equilibrium,
regardless of job and worker turnover costs. This restricts the analysis to the more
empirically relevant scenario where the most productive firms export while the less

productive do not. Because of differences in a manager’s skill, the firms using the

30

same technology produce different levels of output. It may be possible that fixed
exporting costs are such that some firms using the same technology choose to export
and others do not. However the condition on fixed costs given above allows firms to
respond to trade liberalization via technology choice, generating an avenue for labor
market turnover to shape economic outcomes.

To solve for the open economy we can proceed in the exact same manner as
in section 3 where the closed economy equilibrium was characterized. The wage
distribution is still described by (8) and (9). Since Y is not traded in equilibrium
the market clearing condition is unaflected. The difference is that firms in the X
industry now face export opportunities. The zero profit conditions for H type firm

must include trade costs. So (15) becomes

 

 

 

:1
£11 = [6(FH+k)+k7—67k]l(S2,H)+Fx a (19)
CL [5(FL + k) + k7 - 57k] 1 (52, L) (1 + Tl-U)
( [601 + k) + k7 - 67k) 1 ($2.12) * )1” (1+ T1_.)s
[6(FH-l-k) + k7 — 67k]l(Sg,H) + F3;
and the number of firm using the H technology is
00
M
NH = ~ / z (s. H) fH(s)dG<s)
o[6(FH + k) + k7 — 6yk]l(H) +F;C

$2
4.1 Gains from Trade & Openness

Yeaple (2005) studied how firms which do not face the prospect of labor market
turnover will adjust their technology choice in response to a multilateral reduction in
trade barriers. Lower trade costs reducethe skill requirement for managers to find
jobs using the best technology, and raise the skill requirement for participation in the
skilled sector. That is, more production in the X sector occurs at H -type firms, the

firms in the X industry with the lowest productivity shut down, and the Y sector

31

expands as trade raises aggregate income. (When 1 is reduced, SQ falls and $1 rises.)

The reallocation of economic activity within the skill intensive sector toward the
most productive firms increases income inequality, raises average productivity, and
reduces the price of the composite skilled good PX. Nominal skilled wages, which are
skilled wages in terms of the labor wages, of managers with jobs implementing the L
technology fall, and rise for managers using the H technology. Skilled wages respond
this way to trade liberalization because export opportunities raise the demand for high
skilled managers, while demand for workers who are not skilled enough to export will
fall. With the effects trade liberalization well understood in the literature what
remains is to examine how labor market turnover amplifies or dampens these effects.

Job destruction has been shown to deter firms from adopting the best available
technologies. Since the reallocation of production toward more efficient organizations
is the key source of adjustment, the incidence of job turnover diminishes the skilled
sector’s response to freer trade. With high job turnover few firm adopt the tech—
nologies that would grant export opportunities. Furthermore, as trade is liberalized
fewer firms upgrade their technologies in high job turnover industries.

To see this consider equation (19). By differentiating with respect to r we can
show the effects of trade liberalization on the adoption of each technology. The
question of interest here is how the effects of trade liberalization are influenced by
turnover rates. So differentiating again with respect the labor market turnover rates

the next result is established.

Proposition 5 Adjustments to trade liberalization are smaller for industries with a

higher job turnover rate and a lower worker turnover rate.

Proof. The second order derivative with respect to the industry job destruction

32

rate13 is

are) ,. _ -
L _( ’lk(FL FH) 11":t(FL'I'k 71) ) (£11)
3165 — ([5(FH + k) + k7 — Mk] I (82, H) + F3) CL

1(82, H)l(SQ,-H)T_U (1 + 1'1”")-1 < 0
[6(FL + k) + k7 — 67k] 1 (SQ, L) o2

 

Proposition 6 compliments previous new trade theory literature on the effects of
reducing trade costs in industries with heterogeneous firms. In Melitz (2003), Man-
asse and Turrini (2001), and Yeaple (2005) reducing trade costs generates gains by
directing production toward more efficient facilities, driving out less efficient produc-
tion and expanding export opportunities to take advantage of economies of scale.
Expected labor market turnover costs at high and low productivity facilities are key
to establishing the magnitude of the reallocation of production when trade costs fall.
Given the amount of, and variation in, worker and job turnover observed across in-
dustries, and the differences in costs that may arise across countries due to policy,

turnover can play an important role in an economy’s response to trade liberalization.

4.2 Trade preferences

Trade induces a reallocation of production to the most efficient firms and managers.
With lower trade barriers managers that do not participate in export markets lose in
terms of their nominal wages as the demand for their services falls. Total levels of
labor market turnover are reflected in prices. As a result the total levels of worker
and job turnover influence changes in real skilled wages due to trade liberalization.
In this section I consider the effect trade has on real wages to determine the trade
preferences of workers.

Labor market turnover influences trade preferences along two dimensions. The

33

size of real wage gains/ losses from trade depend on industry turnover rates. Also,
an industry’s levels of job and worker turnover determine the share of workers who
stand to gain or lose from free trade. So turnover can affect the intensity of trade
preferences as well as the extent to which trade is favored or opposed.

First consider the trade preferences of laborers and the least skilled managers in
each economy. Labor wages are always equal to the numeraire. Trade does not
change the employment opportunities for labor because they earn the same wage
regardless of their employer. Because Y is not traded in equilibrium, the nominal
wages of the least skilled managers who are self-employed in the Y sector do not
change either. Trade does not affect the nominal wages of labor or the least skilled
managers, but since PX falls with trade liberalization, these workers always gain from
trade.

Now consider managers employed in the skill intensive X sector. Trade liber-
alization provides better export opportunities for the highest skilled managers. As
demand for high skills rise, so do the nominal wages earned by managers at exporting
firms. Price reductions further imply that high-skilled managers always gain in real
terms when trade barriers fall. Managers in the X sector who are relatively low-
skilled may not benefit from trade since they will not participate in foreign markets.
Demand for these mangers who cannot export fall, and so do their nominal wages.
However aggregate prices fall, so the effect on the real wage of the moderately skilled
is uncertain.

Nominal wage reductions will result in real wage losses for the moderately skilled
when trade generatae only small price reductions. At low levels of both job and
worker turnover the share of total output sold in the market (rather than covering
turnover costs) is higher, putting downward pressure on prices. So if consumers
initially face low prices because of low turnover costs, trade liberalization results in

only small price reductions”.

34

Besides total turnover rates, the relative levels of job and worker turnover have
implications for how prices respond to trade. When the skilled sector in the foreign
country exhibits high job turnover, only a few products will be available for import.
The aggregate price index for the skill intensive good is decreasing in the number of
varieties available. Therefore relatively high job turnover causes the price savings of
trade to be small. Hence in a symmetric trading environment moderately skilled
managers will be more opposed to trade when employed in industries with low levels
of both worker and job turnover, but relatively higher job turnover.

Having established when the middle class of managers is likely to lose from trade,
what is left to examine the number of managers who stand to lose, the extensiveness
of anti-trade preferences. Wage reductions occur among the moderately skilled with
trade liberalization because they are employed by firms which adopt technologies that
exclude them from export opportunities. So the extent to which each technology is
used in an industry is the crucial factor for determining the fraction of managers who
stand to lose from trade.

Again using proposition 1, relatively high job turnover increases the share of man-
agers using the L technology. Of course trade induces some firms to begin offering
jobs using the best technology. But with high job turnover the number of new H -
type jobs created after liberalization is small. Hence job turnover increases the share
of managers exposed to the perils of trade, and discourages firms from offering jobs
that would save them. The next proposition summarizes the relationship between

the pattern of labor market turnover and trade preferences.

Proposition 6 Real wage losses from trade are more likely for some skilled workers,
and more common across skilled workers, in sectors with low levels of labor market

turnover but with relatively higher job turnover.

Even in this simple model of exogenous turnover the influence of turnover costs on

firm technology choice suggests an intuitively appealing relationship between labor

35

market mobility and trade preferences. Firm responses in technology choice to trade
liberalization are less harmful when workers are more mobile, have less loyalty to their
employers, or can be replaced at low cost. When jobs survive for only a short time

or costs of restructuring production are high, fewer workers stand to gain from trade.

5 Conclusion

Creating and continually staffing employment positions are costly activities for firms.
Given the observed levels of job and worker reallocation these costs are likely to have
a significant impact on firm behavior. In an economy populated by firms which are
heterogenous largely by choice, systematic variation in turnover rates across industries
suggests that the role of labor mobility should not be ignored. Moreover, job and
worker turnover are distinct economic events. Except in a knife-edge case, where
the cost share of each source of turnover is the same for all technologies, firms will
respond differently to the prospects of replacing jobs and replacing workers.

When jobs using the best technology are more expensive to create, higher levels
of job destruction reduce the incentive of firms to adopt state of the art production
techniques. High job turnover increases income inequality, reduces average industry
productivity, and skews the sales concentration. High job turnover also limits export
participation and industry adjustment to trade.

The pattern of labor market turnover in an industry shapes trade preferences.
A large share of the skilled workforce is made worse off relative to the rest of the
population by international trade when there is high job turnover. Moreover, the
chance freer trade harms these workers in terms of their real wage is greater when

there is little turnover in the labor market, but job turnover is relatively high.

36

Notes

1JEL Classification: F16

2Even the little correlation that is observerd may be overstated due to measure-
ment error.

3This will be shown to be true when worker quits are uncorrelated with managerial
skill, and inversely related with skill because in equilibrium only less skilled workers
use "low" technologies.

4The extention of Yeaple (2005) to production by firms with many employees in
crucial. First, one worker producing a fixed amount of output means that the firm
faces no marginal decision with regard to quantitiy or prices. The result of fixed price
mark-ups over units costs from monopolistic competition and CBS preferences does
not hold. The firm will sell the worker’s output for the maximum price consumers
will pay for the given quantity.

Second, with only one worker, job destruction results in destruction of the firm.
The sunk entry cost would have no effect on firm behavior is subsequent time periods.
In a large firm model, the law of large numbers suggests a pseudo-fixed cost equal to
the incidence of job turnover costs. Thus free entry would lead to firms earning zero
profit in equilibrium

5See Magee (1980), Irwin (1996), Beaulieu and Magee (2004), and Balistreri
(1997), among others.

6By assumption 0 > 1 so that all varieties have positive demand. This also implies
that p 6 (0,1).

7In equilibrium, the allocation of workers to firms using each technology will be
perfectly positively assorted based on skill. There will be no better opportunities for
a worker to earn higher wages, and hence no endogenous reason to quit.

8Again, see Davis, Haltiwanger and Schuh (1996) and Burgess, Lane, and Stevens

(2000) for evidence that turnover rates are heterogenous across industries. Varia-

37

tion does not imply independance necessarily but interindustry links in firm/ worker
turnover rates are outside the scope of this paper.

9Again note that the inequalities result from the assumption that each technology
is adopted by at least some firms. If the sizes of the labor force at each type
of firm were constant, then the inequalities would obtain from the assuptions on
the comparative advantage given to skilled workers using better technologies. High
demand for X is reflected in the size of the labor force used by firms in the X industry
relative to Y.

10The term l (3, -) represents the optimal labor hiring decision of the a firm with

a manager of skill 3, given the optimal choice of technology. This a simplification

OO
32
of notation where is should be understood that / l (3, ) dG’ (s) = f [(3, L) dG(3) +
0 S1
00
f l(s,H)dG(s).
32

11T he distribution of skilled income is given in nominal terms. But since labor
wages are equal to the numeraire good, these results are true when considering both
labor and skilled managers working in an industry.

121 have reverted to the parameterization where worker quits are uncorrelated with
skill. As shown in the previous section, only the magnitude of the results to be
derived are affected by a correlation between worker turover and manger skill.

13Following from proposition 1 the effect of the worker turnover rate is the opposite
of the job turnover rate.

14(Prices are reduced by free trade, (17111er < 0, and (ll—5% is larger in magnitude for

larger values of 6 and 'y.)

38

Cutoff

 

 

 

 

between Y and Entry
x sectors
51
Y-Market
Clearing
S; Cutoff between H

and L technologies

Figure 1.1: Equilibrium Allocation of Managers to Technologies

 

Cutoff
between Y
and X Entry
sectors ‘
51

Y-Market
Clearing

 

 

 

 

$2 Cutoff between H
and L tech

Figure 1.2: Effects of Labor Market Turnover Rates on Technology Adoption

39

Cutoff .’ Aa
between Y and ' -
X sectors

Entry

 

51

Y-Market
Clearing

 

 

 

Cutoff between H
and L tech

 

Figure 1.3: Equilibrium Technology Adoption with Correlation between Quit Rates
and Managerial skill

40

Chapter2
International Trade, Wages, and Unemployment
with Endogenous Firm Scope15

ABSTRACT: Heterogeneous managers match and supervise production
of multiple goods. Managerial skill improves labor productivity, so long
as efficiency wages deter shirking. Trade liberalization eases the effi-
ciency wage constraint, thereby raising total employment and labor wages.
Trade rationalizes production in three ways. Firms become more spe
cialized by dropping marginal product lines. Production is reallocated
within industries toward the most efficient firms. Also trade rationalizes
the matching behavior of managers, leading to improved team formation.
Overall wage inequality rises as trade costs fall. There are workers who

may benefit from trade even though workers with higher skill may lose.

6 Introduction

Two common assumptions in the trade literature are that firms produce a single
product and use factors that are fully employed. Though such models have provided
great insights about the nature of open economies, even casual observation leads to
the conclusion that unemployment and multi-product firms are persistent features
of any economy. While nearly all firms produce many differentiated products, they
vary in both their product scope and productivity. These differences across firms are
likely to result from endogenous choices made by rational economic agents.
Separate lines of literature have examined the impact of trade liberalization on firm
scope and the effects trade has on unemployment in environments with heterogeneous
firms. However, a link between features of structural unemployment and firm scope

has been left unexplored. Here I consider how firms choose the number of products

41

to manufacture given that unemployment persists because labor wages must be high
enough to deter shirking. In addition I examine how the choice of skilled workers
to match determines how firms within an industry initially organize, and shapes the
distribution of firm productivity. Trade has a direct effect on the incentives of labor
to shirk and the matching behavior of managers. In response to a change in the
nature of worker supply after liberalization, firms adjust their product scope, hiring
decisions and factor rewards. Moreover, managers rethink their pre-liberalization
partnerships leading to changes in industrial organization.

Few firms produce only a single product and multi-product firms seem quite con-
cerned with the specific portfolio of products that they offer. Firm behavior across
product lines has been shown to respond to both internal and external influences.
Bernard, Redding and Schott (2008) document the degree of product switching by
multi-product firms and the share of production taking place at multi-product plants.
Using 5—digit SIC classifications to identify different products they find that 87% of US
manufacturing takes place at plants which produce multiple products, half of whom
alter their product mix every five years. The decision to add or drop a product is
often made for reasons particular to a firm/ product pairing. Turning to external
forces, Bernard, Jensen and Schott (2006) provide evidence that plants alter their
product mix when exposed to foreign competition. Baldwin and Cu (2006) also find
that lower tariffs cause plants to reduce the level of diversification in production but
note that exporter plant size does not seem to respond to changes in tariffs.

Political discussions of international trade center on either unemployment or job
quality. Trade can improve, or harm, the economic opportunities of workers in three
ways. First, international market size could impact the probability that each worker
is employed at all. Second, for those who are employed trade may alter the type
of job they obtain. Third, even the workers who retain a certain job type will feel

the effects of globalization if the rest of their employer’s workforce responds to trade

42

liberalization. These issues have been explored previously in Davidson, Martin and
Matusz (1999), Itskhoki and Helpman (2007), Matusz (1986) and (1996), Davidson
and Matusz (2004), Felbermayr, Prat, and Schmerer (2008), Davis and Harrigan
(2007), and elsewhere.

Careful examination of the relationship between trade and labor market outcomes
must account for the relationship that globalization has with both sides of the labor
market: supply and demand. The emphasis of much of the literature falls on the
effects of reduced trade costs on the organization of production, with labor market
outcomes resulting from only changes in firm behavior. Worker behavior is left out
of the analysis. This sort of "partial-partial equilibrium analysis" misses half of an
economy’s trade adjustment’e. Commodity prices and export opportunities are key
determinants of worker supply. Endogenous worker responses to trade liberalization
can play an important role in shaping firm organizational design, overall industrial
organization and labor market outcomes.

Besides multi-product firms and unemployment, another key feature of any econ-
omy is heterogeneous production. Within narrowly defined sectors firms differ in
the number of products that they offer (Bernard, Redding and Schott (2008)), in the
types of workers that they hire, technologies that they employ (Doms, Dunne, and
Troske (1997)), in productivity and in export status (Bernard and Jensen (1999)).
Given the observed patterns of heterogeneity across each of these dimensions, I take
the skill of managerial teams to be the underlying source of firm differences, as in
Lucas (1978) and Rosen (1981). A key difference in the approach taken here is that,
while the distribution of individual managerial talent is exogenous, the distribution
of the skill of management teams available for hire is endogenous. Heterogeneity
results from both endogenous matching behavior and exogenous skill difl'erences17.

In order to address the relationship between trade, worker supply, and the organi-

zation of production, I amend the model set forth in Matusz (1996). He incorporates

43

efliciency wages into a monopolistic competition model with intraindustry trade. La-
borers make a supply decision in the form of whether or not to shirk, as firms have
imperfect monitoring abilities. In each economy a single final good is produced using
the set of domestic and foreign intermediate products available. An increase in the
number of available intermediates allows for greater specialization, and hence greater
efficiency, in the production of the final good.

Heterogeneous intermediate firms have a core variety which they can modify to
supply additional varieties to the market. Each firm is most productive in manufac-
turing its core variety. Labor efficiency suffers when producing additional varieties
because of a greater need for modification. Given diminishing returns to scope,
market demand, labor wages and management skill, each firm determines its scope
endogenously.

Each economy is endowed with a set of managers who are heterogeneous with
respect to their ability to improve labor productivity, given that shirking is deterred.
Firms hire two managers and assign one to supervise labor in perforating assembly
tasks associated with developing the core variety and one to modification activities
necessary to produce additional varieties. As managers cooperate in production of
all the firms varieties, they share the firm’s operating profits. Differences in the skill
intensity of "scope tasks" and "scale tasks" lead to matches between heterogeneous
managers, while complementarity leads to positive assortative matching. Given profit
opportunities and the set of potential matches, skilled individuals form management
teams endogenously.

Trade liberalization induces adjustments in production both across firms and
within firms. The introduction of additional foreign intermediate varieties allows
for greater efficiency in the production of the final good. This gain in efficiency in-
creases real wages and relaxes the efliciency wage constraint. Slack in the efficiency

wage constraint and better access to foreign markets encourages firms to hire addi-

44

tional labor. Additional labor demand bids up labor wages inducing a reallocation in
production. In the face of higher labor costs the least productive firms are forced to
exit and surviving firms shed marginal product lines. A greater share of production
takes place at the firms with the best management teams, who concentrate on their
core specialties, thereby increasing aggregate productivity.

This sort of marginalization of production across and within firms is similar to
results obtained in Melitz (2003), Bernard, Redding and Schott (2006), Eckel and
Neary (2008), and Nocke and Yeaple (2006). A significant difference being that
changes in firm scope and industry organization come at the behest of both firm
and worker response to trade liberalization. The most prominent departure from
previous work is the role that international markets play on the manner in which firm
management organizes initially.

Globalization induces adjustments in managerial matching. As the least efficient
management teams exit, the highest skilled member of those pairs, who initially
would only accept high skill intensity positions, now are willing to accept a less skill
intensive position as opposed to unemployment. In light of a new group of managers
who offer to take low skill jobs, every other manager rethinks her current partnership.
Each manager vies for one of the relatively higher skilled managers willing to take a
low skill intensity job. All surviving firms realize a change in management. Some
individual managers feel the effect of trade via the type of job they acquire, and all
feel its effects through the skill of the partner with whom they match in equilibrium.

When two managers attempt to match with a particular individual, the higher
skilled of the two will always win the bidding contest. So as trade induces relatively
higher skilled managers to begin accepting low skill intensity jobs, they will match
with the best available partners. Adjustments in managerial matching due to trade
lead to more positively assorted matches. Increased segregation generates productiv-

ity gains within the top firms, but losses among the bottom firms. The rationalization

45

of matches at the largest firms may cause them to further diversify, despite the partial
influence of trade to reduce product scope. The complete economic response to trade
is the sum of the effects of matching, firm selection and product selection.

Both changes in production and changes managerial matching have consequences
for total welfare. Even though trade reduces labor productivity partially through
changes in management at smaller firms, in the aggregate these losses are dominated
by the productivity gains from (1) the reallocation of production across firms toward
larger firms, (2) the specialization within firms through decreased product scope, and
(3) increases in the quality of management at larger firms. Thus open economies
enjoy greater economic welfare.

At a minimum globalization has a marginal impact on matching outcomes by
forcing some mangers to take low skill positions. But trade can have a drastic impact
on the formation of management teams by inducing some managers to actually prefer
low skill positions, if doing so guarantees the opportunity to export. Only the most
efficient firms can penetrate foreign markets. So if there is a shift in matching
behavior in order to secure export status, preferences will shift toward matching
with higher skilled partners. Whether the result of changes in matching outcomes
or overall matching behavior, trade causes matches between managers to be more
positively assorted. The effects of shifts in matching behavior are magnifications of
the effects due to marginal adjustments in matching outcomes.

The matching outcome in the manager market is crucial to the skilled wage distri-
bution. For either job type, better partners result in better wages. More segregated
matches after trade is liberalized increase the wages of the top managers but reduces
the wages of the lower skilled. Real wage losses are more likely when matching
preferences shift than when there are only marginal adjustments to matches.

Managerial wages also depend on market share and export status. Better trading

opportunities benefit the best management teams through the reallocation of pro-

46

duction; with heterogeneous matching the best teams are not composed entirely of
the most able managers. The group of relatively low skill managers employed by
exporting firms will benefit from trade, while some higher skilled managers with skill
intensive positions at non-exporters will be harmed.

The combined effect of adjustments in the management and adjustments in pro-
duction lead to an ambiguous effect of trade on the wages for all but the most skilled.
The highest skilled workers always gain from trade and as a result overall wage in-
equality rises. The pattern of rising wage inequality that emerges post trade liberal-
ization is one of less within-firm wage dispersion and more inequality across firms for
workers with similar skill. These predictions are consistent with Dunne et al. (2004)
who document the contributions of within—firm and across firm wage dispersion for
production and non-production workers in the US. In addition moderately skilled
workers may gain from trade, although the likelihood of benefiting from globalization
is not necessarily increasing in skill.

Labor always benefits from trade. The introduction of foreign varieties and the
rationalization of domestic production lowers prices thereby increasing the real wage.
Increased labor demand further bids up nominal wages and raises total employment.
Thus labor benefits from free trade because of better compensation while employed,
and from shorter expected durations of unemployment.

The next section describes the model of labor and goods markets. Section 3
discusses the matching behavior of potential managers and derives an open econ-
omy equilibrium. Section 4 discusses the impact of a reduction in trade costs on

production, managerial matching and labor market outcomes. Section 5 concludes.

47

7 Model

7. 1 Production

The world consists of two countries. Each economy produces a single final good Y
using the set of available intermediate goods from domestic firms, x, and exported by
foreign firms, sz. (An asterisk denotes a foreign variable.) Because firms produce
multiple products the mass of varieties of intermediates available, x, is greater than
the mass of active firms determined below. The final good is assembled costlessly

by combining intermediates according to the production function

1/(9

Y = /r?dj + / xgdj , a 6 (0,1) . (20)
X is.

Each intermediate good is produced by a firm, which may produce multiple interme-
diate varieties, using labor and managerial skill. There are two necessary tasks that
must be performed by a firm producing any intermediate variety. First, labor must
be used to assemble a "core" intermediate that represents the firm’s base product in
which it has the most expertise. This task is called an assembly activity. Each unit
of output produced, of any variety, requires one efficiency unit of labor to perform
the necessary assembly activities.

Second, if the firm produces multiple varieties additional labor must be used to
alter the characteristics of its core intermediate to contribute to the production of
Y. This task is called a modification activity. The further a particular intermediate
variety is from a firm’s core variety, the more labor that must be used in modification
activities for that specific variety. For simplicity I assume that if a firm produces a
mass of intermediates N, indexed by their distance from the core variety at n = 1,
then the variety n E [1, N] requires n efficiency units of labor to perform the requisite

modification tasks. Modification activities are particular to the characteristics of

48

each specific intermediate good. Producing additional varieties has no effect on the
efficiency of labor in the production of the firm’s inframarginal varieties.

The labor pool has mass A. The productivity of labor in performing both activities
is normalized to unity. That is, each laborer supplies a single unit of efficiency labor
of his own accord. Each economy is also endowed with a mass p of heterogeneous
agents who differ in their Skill, 3, for managing labor. A manager can improve
the productivity of labor in performing either assembly or modification activities
according to her skill levells. While working under a manager of Skill 3 each laborer
supplies m (3) efficiency units of labor to completing modification activities and f (s)
efficiency units of labor to performing assembly activities. More skilled managers
are better at increasing the productivity of labor; m’ (s) > 0 and f’ (s) > 0. The
distribution of managerial skill is given by G (3) with support (0,S], and S can be
arbitrarily large.

Managerial tasks differ in their skill intensity. I assume, without loss of generality,

that the assembly task is more skill intensive”; that is (figfi; > %%. If

120, then the optimal strategy will be to

a firm hires two managers of different skil
assign the more skilled manager to the more skill intensive task of improving labor
productivity in completing assembly activities. The labor needed to produce one

unit of variety n, which is a measure n — 1 from a firm’s core competency, produced

under the supervision of managers with Skill 3’ and s”, where 3’ < 3”, is given by

 

 

l(n)=[ ", + 1 j (21)

49

7.2 Demand

The composite final good Y is the numeraire. Combining intermediates according

to (20) yields a cost function for Y given by

(61-1)

9 _ * s
0(3)”) = /P,I6‘155j+ /PjI6‘15dj Y (22)

X ng

The total sets of available intermediates from domestic and international firms are en-
dogenously determined by the number of active domestic firms, foreign exporters, and
the number of intermediates that each firm produces and exports. An intermediate

firm faces a demand for each individual variety n of

 

__a__. . ,. a T ,
Dn—Y /P,(9_1’dj+ / ij‘lldy Mala-7+
X ng
_ _1 _
* 6 0 7 1
1(a) 1” [Pr 6—1)dJ+/Pj(6_1’dj 180016:I
x* Xex
l. ..

 

 

The variable I (n) is an indicator which equals 1 if the firm exports variety n and 0

if it does not.

7.3 Firm behavior

The gain in efficiency in producing the final good from having a greater mass of
intermediate varieties guarantees that no firms will enter and produce the same in-
termediate goods. Also each firm is small relative the whole market and so takes
the prices of other varieties as given. Similarly the firm can ignore the effect that its

own additional production lines have on the demand for its inframarginal products.

50

The profit function for an intermediate firm is equal to the revenues from all of its
product lines (N), for all units of each variety sold (:1: (n)) , less labor costs per unit of
output of each variety (at labor wages w), beachhead costs for the firm ([3) and per
product (7) if the firm exports, and total wages paid to managers for services on all
varieties (Wm and Wf). Implicitly defined for the skill of managers hired, the profit

function is

N*

N
H = / lp(n) — or (n)) (n, an + / I (n) {lp*(n) — or (n)) (n) — 7} an
‘1 '1
_I(1)f3_Wm—Wf

Managers perform identical tasks across all intermediate varieties produced by
the firm, and so their compensation (described in detail below) does not affect firm
behavior at the margin. Each firm maximizes profit by choosing the price it charges
for each intermediate variety, and the total number of varieties to manufacture. Of
course the optimal choice of scope and price depend on the skill the managers hired.
The first order condition for the domestic price charged by a firm with managers of

skill 3' and s”, with 3’ < s”, is

 

 

(",+ 1]. (23)

Each firm charges a fixed mark-up over marginal costs, which are a function of labor
wages, or, and labor productivity, the term in brackets. The first-order condition
for the optimal firm scope shows that firms add production lines until the marginal

intermediate variety yields zero additional profits.

(s (N (s'. s”)) — .1 (N (s', s”))1 . (N (s'. s")) = o (24)

51

Free entry guarantees that prices and scope are chosen optimally:21 and that all
revenues accrue to either labor or managers. Then using (23) and (24) the total

labor demand of a firm with managers 3’ and s” , with 3’ < 3”, is

IV (3,,8”)

L (3’, s”) = / l (n) [1:(n) + 13* (n)]dn

H111 labor employment in this economy would be / l ,- dj = A, where the labor demand

X
for all intermediates produced in each country required use of the entire labor pool.
However the interest here is in equilibria where / lj dj < A.
'X
7.3.1 Export Choice

If an intermediate firm exports it must pay a fixed cost )3 to acclimate itself to foreign
markets and 7 to prepare each of its products for use in foreign production of the
final good. In addition the firm must pay iceberg transportation costs on each unit of
output exported. For a single unit of a specific variety to arrive in a foreign market
an exporter must produce and ship 7' > 1 units. Fixed exporting costs have no effect
on the marginal behavior of firms, and as a result a firm that charges a price p in the
domestic market will charge rp in the foreign market.

Each intermediate firm must decide whether or not to export at all, and if so
which products to sell overseas. Average fixed exporting costs are decreasing in the
number of products exported because the firm must only make the investment to
learn about foreign markets once. Because of the need for modification, each firm
experiences diminishing returns to scope. The trade-off between reduced costs of
market penetration and diminishing profits defines a firm’s optimal export strategy.

A firm that makes N intermediate varieties will be an exporter if, for at least one

52

n E [1, N], the follow criterion is satisfied

[12* (n) — rl (n)] 113* (n) 2 {3 + 7n (25)

f—‘\.:

Upon entering a foreign market the firm must determine its extensive export
margin. The firm chooses the number of products to export by comparing mar-
ginal operating profits from exporting an additional product and the marginal cost
of adapting the product to the tastes of foreign consumers. So a firm will export the

varieties [1, Nat] , where Neg; satisfies
IP*(N6:1:) — 71(Nexll 35* (Neat) = ’T- (26)

Of course New g N. Figure 2.1 shows the optimal scope and extensive export margin
established in (25) and (26). Firms that do not export would have an operating
profit curve that lies entirely below the line representing fixed exporting costs. As
drawn the firm in Figure 2.1 would not choose to export only its core products, even
though it produces them most efficiently. For this firm, decreasing average fixed costs
to penetrate foreign markets is crucial in the decision of whether or not to export.
The last thing to notice about Figure 2.1 is that because managerial skill is relatively
more important for intermediates that require more modification, firms with better
management are more likely to export and will export a greater range of intermediate
goods. That is, better management shifts the operating profits curve for a firm up.
Also better management reduces the firm’s incidence of diminishing returns to scope,

which would be illustrated by less curvature in the operating profits curve.

53

7.4 Factor Markets
7.4.1 Efficiency Wages and Labor

Managerial skill improves labor productivity so long as labor is putting forth effort.
Working on any task, at any level of productivity, is onerous so that each laborer has
an incentive to shirk his duties while enjoying wages. Firms pay efficiency wages, to,
that are higher than the opportunity cost of effort and fire labor caught shirking. The
benefit of higher wages and the threat of unemployment deter shirking in equilibrium.

The model of the labor market is set in continuos time. Labor who put forth effort
still face the probability b > 0 that their employment will be terminated exogenously.
Employees who shirk their duties are caught with probability q > 0. Note that
these probabilities (particularly q) are not functions of managerial skill. The role of
skill in this model is only to improve labor productivity in the performance of certain
tasks. Regardless of skill in supervising modification activities or assembly activities,
all managers can monitor labor with the same ability.

Labor can be in one of three possible states: employed and putting forth effort,
employed and shirking, or unemployed. Laborers are risk neutral and find jobs at
an endogenously determined rate e. All laborers discount the future at a rate p > 0,
and the disutility of effort is d > 0. The asset value equations for being in each state

are

pVe = w—d+b(Vu—Ve)
pvls = w+(b+9)(Vu—Vs)

Pvu : €(Ve—Vu)

Shirking is avoided in equilibrium so long as the expected lifetime utility of shirking
today is less than the expected utility associated with putting forth effort, that is

Ve 2 V3. Profit maximizing firms will pay efficiency wages just high enough to deter

54

shirking so that V8 2 VS, or

 

w=d(p+b:q+e) (27)

In a steady-state equilibrium the flows of labor into and out of employment are
equal. Since shirking is deterred in equilibrium, the flow out of employment comes
only from exogenous layoffs. A fraction b of the total number of workers employed,

/ ljdj, transition out of employment, while a fraction e of the pool of unemployed
X
labor, A — / ljdj finds a job. Thus in a steady state

X

7.4.2 Managerial Earnings

Production occurs as managers cooperate in the performance of specific tasks, super-
vising either modification or assembly activities. Firms cannot capture any surplus
generated from production because of free entry. Were any economic value retained
by a firm, a competitor could poach the firm’s management by offering marginally
better pay. So total managerial earnings are the operating profits (revenues net labor
costs and exporting costs if applicable) from all of the firm’s varieties. Operating
profits for a firm which employs managers with Skill 3’ assigned to modification ac—

tivities, Skill 3" assigned to assembly activities, and produces N (3', 3”) varieties of

55

intermediate goods, are

 

 

rv(sfls”)
7r (5’3”) = / (pm) — to (mill) + f (:,,)]) a:(n)dn+
l
rv(sfls”)*

 

 

Note that the first argument in 7r (-) refers to the skill of the manager assigned to
modification tasks, and the second argument to the manager assigned to assembly
activities.

The coalition of managers must decide how to divide the sum of operating profits
among themselves. Here I use the Shapley Value to determine the allocation of
operating profits across the two managers. Each manager earns the average of her
marginal contribution to the coalition. That is, each manager earns the average of
operating profits when working with another skilled manager, and operating profits
when her counterpart’s labor activities are unsupervised.

When working alone, a manager of Skill 3' assigned to modification activities
generates 7r (3', 0) in operating profits, and an assembly manager of skill 3” generates
7r (0,3”). Therefore a modification manager contributes 7r (3’ ,0) to the coalition
without a partner, and 7r (3’, s”) — 7r (0, 3”) working with her partner. Then taking
averages, managerial earnings for the modification manager and assembly manager

(using a similar derivation) are respectively

I ll 1 r I II II
VVm(3,3)=§{7r(s,0)+7r(3,3)—7r(0,s )} (29)

w, (3', 3”) = % {7r (0, s”) + 1r (5', s”) _ 7r (3', 0)} (30)

56

8 Equilibrium

8. 1 Managerial Matching

Two important features of the allocation of operating profits to management in (29)
and (30) determine managerial matching behavior. First, as a manager’s own skill
level increases so does the opportunity cost of not cooperating with a second manager.
Put another way, the managerial compensation functions are supermodular22. Each
manager’s earnings increases with the skill of her partner. As a result the equilibrium
matching pattern is some type of positive assortative matching where, all else equal,
each manager prefers a relatively higher skilled partner.

Second, managerial compensation depends not only on the skills of the two man—
agers but also the task to which each is assigned. Still assuming (WLOG) that the
assembly task is more skill intensive, if two managers of the same skill match and
cooperate in production, the manager assigned to supervise assembly activities will
earn a strictly greater wage than the manager assigned to modification activities.
In a homogeneous match the manager assigned to the less skill intensive task would
prefer to match with a marginally less skilled worker to obtain a more lucrative skill
intensive management position. Therefore, with a continuous distribution of skill,
equilibrium matches will be heterogeneous23.

A tendency towards positive assortative matching leads to equilibria that are more
segregated; managers matching with others who have similar skill. The returns from
the skill of a partner encourage behavior that leads to segregated matches. On the
other hand post-match task assignment across different skill intensities encourages
behavior that leads to heterogeneous matches. The particular matching outcome
sustained in equilibrium depends on the primitives of the model: the skill distribution,
world market size, fixed exporting (beachhead) costs and variable trade costs. The

interest here is on trade costs. An important distinction exists between shifts in the

57

matching regime sustained in equilibrium, and marginal adjustments in matching
outcomes within a particular regime, that occur at the behest of trade liberalization.

All matching regimes are characterized by a degree of segregation. Given the
complementarity of managerial skill, a more diffuse skill distribution induces behavior
that leads to a more segregated matching regime (see Kremer and Maskin (1996) and
Legros and Newman (2002)). The reason being that a more diffuse distribution of
skill means that ceteras parabis heterogeneous matches will occur between managers
with greater differences in skill. Complementarity makes such matches less viable
even when differences in the skill intensity of managerial tasks exist.

Larger international markets increase the opportunity costs of rejecting higher
skilled partners (in order to obtain skill intensive jobs), especially when doing so
excludes a manager from export opportunities. Trade costs have a similar effect as
international market size on the equilibrium matching regime. Both beachhead and
variable trade costs limit participation in foreign markets and lower the operating
profits of exporting. Reduced trade costs increase the incentives of managers to
overcome the expense of penetrating foreign markets; for some managers this may
mean accepting less skill intensive jobs in order to match with partners that allow
for profitable exports. Hence lower trade costs can lead to adjustments in matching
regimes towards one which is more segregated.

Since there are may potential matching patterns, the procedure here will be to
derive the effects of trade liberalization in the context of a particular matching regime.
Then given the discussion above, describe the new equilibria obtained after trade costs
fall and the economy moves across matching regimes. I choose the most extreme
form of heterogeneous matching where every manager strictly prefers to obtain the
skill intensive position within her employing firm, regardless of export opportunities
afforded at a given level of trade costs, and for all potential skill levels of partners.

As each manager seeks the most skill intensive of the two available job types, the

distribution of skill will be completely bifurcated with respect to task assignments.
The top half of managers will obtain the most skill intensive jobs. The most skilled
manager in the economy will attract the most skilled partner who takes a low skill
intensity position; this must be the median worker24. Then as all managers vie for
the best partners, matches are positively assorted across the median. This matching

regime has been labelled median matching.

8.2 Median Matching Equilibrium

The next step is to derive the endogenous distribution of management skill employed
in a median matching regime. The set of managers that are employed in equilibrium
must be rational in terms of entry and consistent with median matching. The lowest
skilled manager to find a job, S L, will obtain a low skill intensity position supervising
modification activities. In a median matching regime the S L manager will be matched
with a median-skilled manager, SM, who performs assembly services. Entry by a
firm which hires managers S L and SM must be rational given fixed entry costs F,

and the exogenous probability that a firm breaks apart25, b. So,
00
VEntry E /exp(—bt)lI (51.314) dt — F 2 0 (31)
'0

and in equilibrium (31) holds with equality.

A median-skilled manager could also obtain a job supervising modification activ-
ities while working with the highest skilled manager in the economy, S. Therefore,
in equilibrium the median worker must be indifferent between her compensation as a

modification manager and an assembly manager.

Wm (3,4,3) — W (51,, SM) 2 0 (32)

The equilibrium conditions (31) and (32) can be plotted in a two dimensional skill
space with the vertical axis representing the skill level of the manager assigned to the
skill intensive task (assumed to be the assembly manager) and the horizontal axis
representing the skill level of the manager assigned to the low skill intensity task.
Both curves are monotonically decreasing; i.e. 531%? < 0. Fhrthermore, the entry
condition is everywhere steeper than the wage indifference condition (see appendix).
Hence, these two determine a unique equilibrium pair S L and SM.

Since labor is identical across all firms, the distribution of managerial skill em-
ployed in equilibrium (G (s) over [S L ,S] ), and the pattern matching between man-
agers (median matching) completely describe the set of intermediate good firms active
in equilibrium. From this point forward I simplify the notation by indexing each firm
by its highest skilled manager so that the distribution of active firms is written G (s)
with the endogenously determined support [SA/1,3. It should be understood that a
firm of skill 3 refers to a firm with a modification manager of skill (p (3) and an as-
sembly manager with Skill 3 where (,o (-) is the one—to—one correspondence of matches

across the median with 99’ (~) > 0.

8.3 Labor Market Equilibrium

A steady-state equilibrium in the labor market is characterized by an efficiency wage
that deters shirking and a level of unemployment. Combining (27) and (28) the
relationship between the efficiency wage and unemployment rate is given as a function
of the set of intermediate firms active in the domestic country. Then denoting a
representative domestic firm with management skill S R, an equilibrium in the labor

tnarket must satisfy

 

w=d+ (2+qu(1f93))d' (33)

60

The unemployment rate26, u (53) = (A — 5L (53)) /A = A — fljdj /A, depends

X
on both the number of firms and the representative skill level which determines firm

size. The number of firms is increasing in the mass of potential managers, )1, and
the average size of firms in increasing in the skill level of the representative firm,
53. And so the unemployment rate is decreasing in both ,u and SR. From (33) the
efficiency wage paid to laborers is decreasing in the unemployment rate (increasing in
p and S R) because longer spells of unemployment entail greater opportunity cost of
shirking, diminishing the need for higher wages. The LL curve in Figure 2.3 traces
the set of efficiency wage and representative firm skill pairs that are consistent with
a steady—state equilibrium where shirking is deterred, given the distribution of firm

productivity in a median matching regime.

8.4 Goods Markets Equilibria

An equilibrium in the final and intermediate goods markets consists of intermediate
firms setting prices that satisfy (23) and choosing a scope of intermediates accord-
ing to (24), equilibrium matching by managers determined by (31) and (32) in a
median matching regime, and cost minimization in the Y sector according to (22).
Substituting the individual firm prices into the cost function of Y in (22) gives the

zero-profit condition for the Y sector.

/(—)r/(—)r

X X21:

Instead of using the cost for each intermediate product, averaging the zero profit con-
dition across all firms yields a simple expression for the relationship between labor

wages and representative skill level of active management teams. The representative

61

firm from the mass of If management teams produces N (S R) varieties of intermediate
goods which require and average of N (SR) efliciency units of labor for modification.
The firm sells its goods at an average price of “fl (N (3113)). Rewriting the zero
profit condition for Y, given the optimal behavior of intermediate firms and the equi—
librium distribution of active management teams, equilibrium in the goods market

must satisfy

1—6 ~ ~ 0 9 ~ ~ 9 1—6
To(N(SR)1(N(3R))9—:1+ra——IN(3;,)1(N(3;,))9:1( . (35)

(U:

ml“:

8.5 Full Equilibrium

The closed economy is in full equilibrium when both labor markets and goods markets
are in equilibrium. A matching equilibrium occurs at the intersection of the entry
condition in (31) and the median indifference condition in (32), as in Figure 2.2.
Given the distribution of active firms and management teams the labor market and
goods markets are in equilibrium when both (33) and (35) are satisfied. For given
factor endowments A and ,u, an equilibrium is a unique efficiency wage, unemployment
rate and a median skill level. The median skill level implies a certain profile of firms
that can be summarized by a representative skill level. Figure 2.3 illustrates the

equilibrium in the goods and labor markets.

9 Trade

9.1 Liberalization and Adjustment in Production

Regardless of the trading opportunities of an economy labor must be deterred from

shirking in order for production to take place. Changes in trade costs have no impact

62

on the labor market equilibrium conditions. However the equilibrium conditions for
the intermediate product and final goods markets in (35) are dependant on the level of
trade costs. Lower variable costs result in lower costs of imported intermediates and,
because of selection into export markets, a greater number of foreign intermediates
available for domestic production. Both act to lower production costs of the final
good. Zero profits in the final good sector are restored only by an increase in labor
wages. The shift in the goods market equilibrium condition resulting from trade
liberalization is illustrated in the second diagram in Figure 2.4.

The new equilibrium occurs where the shifted GG curve and LL curve intersect.
Holding managerial matches fixed liberalization increases the skill level of the man-
agement team at the representative firm. The increase in average labor productivity
for a fixed set of employed managers has two potential sources: a greater share of
production is taking place at firms who hire superior management teams, or firms
have dropped fringe product lines which are produced less efficiently. In fact, both
occur as a result of trade liberalization.

Lower trade costs increase foreign demand for the varieties exported by domestic
firms, causing these firms to expand the scale of production. The introduction of
more foreign intermediates into the domestic market lowers the relative demand for
the varieties produced by non-exporters, who respond by contracting the scale of
production. Because the most efficient firms are those which export, the result is a
larger share of production taking place at firms with better management.

Adjustments to production also occur within each firm, even without changes in
management. Higher labor wages reduce the profitability of all product lines for both
exporting and non-exporting firms. Non—exporters drop marginal varieties that are
not profitable in the face of foreign competition and higher labor wages. Exporters
are also induced to shed products in the face of higher labor costs, even though

liberalization induces firms to export a larger fraction of the varieties it produces.

63

As these firms drop the products that they make with the least efficiency, average
labor productivity rises. The next proposition summarizes the findings on the effect

of trade on the nature of production.

Pr0position 7 Holding fired the set of managers employed, trade induces an increase
in average productivity both across firms and within firms. After liberalization a larger
share of production takes place at the most eflicient firms and all firms devote a larger

share of resources to the production of varieties in which they are most efi’icient.

9.2 Liberalization and Labor Market Outcomes

Production of the final good is less costly in an open economy. An increase in the
real wage eases the efliciency wage constraint, and together with the fact that a repre
sentative firm has greater productivity, firms demand more labor. Increased demand
bids up nominal labor wages, further benefiting labor. Besides better compensation
when working, spells of unemployment are shorter. At a higher real wage the op-
portunity cost of being caught shirking is much higher. So firms can hire more labor
and feel confident that laborers will exert themselves during production. Hence all

laborers benefit from higher wages and lower unemployment, as in Matusz (1996).

9.3 Liberalization and Adjustment in Management

Trade Liberalization causes a reallocation of production towards firms which employ
better managers. Smaller market shares and higher wages force the least productive
management teams out of the industry altogether. The breakup of low skilled teams
causes a change in the matching outcome in the entire manager market. The lowest
skilled managers can no longer find partners and become unemployed. But their high—
skilled counterparts seek out new matches, accepting low skill intensity positions if

they must. The small group of managers now willing to accept low skill positions

64

causes every other manager to rethink their current partnership.

Equilibrium in the manager market in a median matching regime occurs when
entry is rational and the median manager is indifferent between a low-skill and high-
skill intensity position given her potential matches. The equilibrium condition on
entry shifts up when trade is liberalized because at higher wages better management
is needed to survive. The level of trade costs also has an impact on the incentive com-
patibility constraint for the median skill level. Better export opportunities increase
the operating profits from participating in international markets. Furthermore lower
market shares for domestic firms reduce the incentive to accept low skill partners.
Each of these incentives cause the equilibrium condition on the median manager in
equation (32) to shift up. The size of the shift in the incentive compatibility con-
straint is larger than the shift in the entry condition because it accounts for both
higher wages and better export opportunities. The first diagram in Figure 2.4 shows
the unambiguous effect of trade on the matching outcome in a median matching
regime.

Lower trading barriers cause matches to become more positively assorted. The
managers with skill above the median level obtain partners ordered higher in the skill
distribution, while lower skilled managers (if still employed) must accept partners
lower in the skill ordering. Those with skill slightly above the initial median level
obtain better partners, but switch to low skill intensity jobs, per the incentive com-
patibility constraint on the median manager. By accepting the low skill intensity job
they gain access to foreign demand and avoid unemployment. The managers with
the lowest skill continue to exit the industry and the remaining managers continue
to reform teams until equilibrium is restored. The effect of trade on the median
matching outcome is depicted in Figure 2.5.

Each manager’s skill level is fixed, so when one firm shuts down the managers who

remain above the median skill level obtain a partner who is the next highest in the

ordering of skill to her initial partner. However the cardinal change in skill depends
on the overall distribution of managerial ability. The next potential partner could
have significantly more skill than the pre—liberalization partner, or could have exactly
the same skill level if there are many identical managers. Because of complementar-
ity of skill in production, more positively assorted matches result in higher average
productivity.

In a peculiar case, where more than half of the set of managers have identical
ability with at least some managers of greater skill, trade results in a change in
matching outcomes that produces results akin to Melitz (2003). With endogenous
matching, trade liberalization results in the top skilled managers finding partners
that are ordered higher in the skill distribution. But if there is no difference in their
partners’ cardinal ability”, then there is no change in the skill of the management
teams which are active in equilibrium both me and post-liberalization. Yet trade
improves overall productivity by driving the least efficient firms out of the industry
and allowing the most efficient firms to expand production.

In the previous section the effect of trade liberalization on the share of production
taking place at the most productive firms, and the level of diversification within
firms, leads to an equilibrium in which the representative firm appears to be managed
with greater skill. Now considering the general equilibrium adjustment to trade, all
firms still operating are in reality managed by higher skilled teams. Endogenous
adjustments to matching in the manager market, and the resulting distribution of
firm productivity, might overturn previous conclusions about the effect of trade on
firm scale and scope reported in Proposition 1, as well as in Bernard, Redding and
Schott (2006), Nocke and Yeaple (2006) and Eckel and Neary (2008). The partial
effect of trade is to rationalize production both across firms and within firms. However
the change in the initial formation of firms causes matches to occur between partners

with more similar skill levels. Better management leads to greater diversification,

66

even when trade reduces the profitability of marginal product lines.

To this point I have discussed the effect that trade has on the matching outcomes
holding the behavior of managers constant. Specifically I have assumed that a
median regime occurs in equilibrium because of every manager’s preference to obtain
a high-skill intensity position regardless of export opportunities. Depending on
the skill distribution, lower trade costs might cause managers to reprioritize and
seek participation in international markets, no matter the skill intensity of the job
obtained. When the behavior of managers changes, the entire matching regime shifts.

Although the matching regime sustained in equilibrium depends on the underlying
distribution of managerial skill, the impact of trade on the matching regime (if any)
is clear. The firms that are able to export are those that have the best management
teams. So if managers change their behavior, their preferences will always shift
toward higher skilled partners, rather than skill intensive jobs. Managers will be more
positively assorted and the complementarity of skill in production implies that the new
regime will lead to a population of firms with higher average productivity. Davidson,
Matusz and Shevchenko (2008) show in a search environment that free trade can
change the behavior of workers so they begin to reject less efficient technologies.
Their result is similar to shifts in matching preferences but only accounts for two
worker types, rather than a continuum of skill levels.

To compare changes in matching outcomes within a regime to shifts across match-
ing regimes consider how each affects the ordinal differences in the skill of the partner
matched with the highest skilled manager, S. Looking within a regime, the exit of a
single firm allows her to match with the manager who has the next highest skill of her
previous partner. But a change in preferences towards export opportunities increases
the desire of others to match with a manager with high skills such as S. The shift
in preferences works to her advantage and she may be able to obtain a match with a

manager ordered several places higher than her pre—liberalization match. Marginal

67

adjustments in matching outcomes within a regime, and regime shifts due to match-
ing behavior, have the same qualitative result: active management teams with higher
average productivity. Although, changes in matching regimes induce a much greater
reallocation of resources. The next proposition summarizes the effect of trade on the

formation of management teams.

Proposition 8 Lower trade costs cause management teams to be more positively as-
sorted and thus raise aggregate productivity. The impact of trade is much larger if

managers change their behavior and prioritize export opportunities over job type.

The rationalization of matches between manager leads to changes in the distrib-
ution of firms that is consistent with the evidence. As demonstrated in Head and
Ries (1999), the number of firms active after trade liberalization falls, and the re-
maining firms are larger on average. Furthermore Nocke and Yeaple (2006) show
that the shape of the distribution of firm productivity changes as the world economy
becomes more integrated. Specifically they show that the distribution of firm sales
within US. industries have become less skewed as trade costs have fallen, i.e. the
largest firms do not lie as far ahead of their competitors when operating in industries
with more trade exposure. N ocke and Yeaple also consider multi-product firms in
their explanation of the "globalization-skewness puzzle". Yet their model predicts a
negative correlation between a firm’s scale and scope. Bernard, Redding and Schott
(2006) find a positive relationship between a firm’s extensive and intensive margins
when looking at US manufacturing.

Adjustment in firm management across the industry has far reaching consequences
for the distribution of firm productivity. Furthermore a reduction in the skewness of
the productivity distribution is consistent with adjustments to matching outcomes in
a median matching regime for many common skill distributions. When the median of
the skill distribution lies near a mode, the top managers will match with a commonly

occurring skill type. Globalization allows the top managers to begin matching with

68

those ordered higher in the skill distribution. But with so many potential matches
with similar skill levels, the top managers enjoy only modest gains in the cardinal
ability of their partners.

The managers who lie above the median skill level, but not at the top of the skill
distribution, will also match with managers ordered higher in the skill distribution.
The increase in their partners’ cardinal abilities will be much greater because they
were matched will less commonly occurring skill types. The most productive firms
are those that employ the best managers. Since these firms experience only modest
gains in productivity from increases iri matches, relative to less efficient firms, trade
liberalization initiates a shift in the distribution of firm productivity that is less

skewed, as in Nocke and Yeaple (2006).

9.4 Liberalization and Wage Inequality
9.4.1 Inequality across Skill Levels

There are two reasons that trade costs affect the income distribution within a partic-
ular matching regime. First, trade liberalization causes a reallocation of production
towards the best management teams. The increase in the relative demand for the
managers who export changes the distribution of income. Second, the formation of
management teams is affected by trade costs. Each manager’s compensation depends
on the skill of her partner, so changes in matching outcomes also affect the income
distribution. The full response of wages to trade depends on the joint responses
along these two avenues.

Better export opportunities increase the operating profits for firms efficient enough
to access foreign demand. However increased foreign competition reduces the relative
demand for intermediates produced by non—exporters. The wages paid to the best
management teams increase relative to wages paid to non-exporting teams. In a me-

dian matching regime teams are formed by heterogeneous managers. Thus relatively

69

higher wages paid to exporting teams are not concentrated among a conjoined skill
group. The highest skilled workers above the median join with the highest skilled
workers below the median and engage foreign markets. Holding matches constant, the
least skilled managers who are still above the median (these are the managers with
skill intensive positions at non-exporting firms) are harmed by trade, even though
managers with less skill gain. The next lemma summarizes the effect that trade has

on the income distribution via the reallocation of production across firms.

Lemma 1 Trade causes a reallocation of production across firms. The effects
on the income distribution is for some managers above the median skill level to lose,
while some below the median will gain. Furthermore the most skilled managers, who

obtain skill intensive positions at erporting firms, gain relative to all other managers.

As some firms drop out of the industry each manager rethinks her current part-
nership and the result is a new matching outcome that is more positively assorted.
Any manager who still obtains a high—skill intensity job after a reduction in trade
costs will be matched with a higher skilled partner. Likewise, all managers with
low-skill intensity jobs will have lower skilled matches than their pre—liberalization
partner. The subsequent impact on wages is clear. Better matches result in better

wages.

Lemma 2 The effect of changes in the matching outcome due to trade liberal-
ization is that the top of the skill distribution benefits from better matches, while the

bottom half of the distribution loses.

In order to describe the total impact of trade on the income distribution in a me-
dian matching regime there are four classes of skill to consider; managers are divided
by the median skill level and a threshold separating non-exporters from exporters on
either side of the median. Of course these partitions are determined endogenously,

but considering the impact of trade within each class of skills is a convenient way to

70

expose the impact of trade on wage inequality. The overall effect is derived from the
combination of the previous two lemmas.

The most skilled workers, above the median and export threshold, benefit from
trade because of both better matches and greater demand for their exported products.
Those managers above the median skill level who do not export are harmed by foreign
competition and decreased market share, but they do benefit from better matches.
The net effect on the real wage of managers above the median who do not export is
ambiguous. However, their wage definitely decreases relative to those at the top of
the skill distribution.

Managers below the median have low skill intensity positions. If they are em-
ployed by an exporting firm, then greater export opportunities tend to increase their
wages. However the rationalization of matches lowers their wages. Again, the net
effect on the wages of exporting managers in low skill intensity positions is am-
biguous; depending on tradeoff between higher export profits and matching with a
lower skilled partner. Their wage decreases relative to the top of the skill distribution
necessarily. Finally, the least skilled managers are harmed by trade both because
of decreased demand for their products and because of worse matching outcomes.
Trade harms the lowest skilled managers in terms of their real wage. Altogether the

effect of trade on the income distribution is stated in the next proposition.

Proposition 9 Trade increases overall income inequality. In terms of the real wage,
the least skilled managers lose, the most skill managers gain, and the impact on those
with moderate skills is ambiguous. Yet all managers lose relative to the top of the

skill distribution.

An interesting result is the likelihood that a manager benefits from trade is not
necessarily increasing in her skill level. If adjustments in matching outcomes are small
then managers with skill intensive jobs who do not export are likely to oppose trade

liberalization, while some workers with less skill would support freer trade. Individual

71

trade preferences depend on both the characteristics of the individual manager and
with whom she works.

Clearly the response of matching behavior to trade liberalization is an important
avenue for productivity gains and the shape of the skilled wage distribution. If trade
initiates a shift in the matching regime towards one that is further segregated, wage
inequality increases much more drastically. As higher managers begin to accept
low skill positions, export profits are concentrated among only the highest skilled
managers. Lower skilled managers are more likely to be excluded from export profits
because of relatively lower skilled partners. Whether due to changes in matching
outcomes or matching preferences, trade initiates a change in the skilled distribution
toward one that is more unequal. Changes in the behavior of managers cause larger

shifts.

9.4.2 Inequality within Firms

The previous discussion of wage inequality was concerned with wages across skill
levels. Trade also causes changes in the relative wages within firms. As trade changes
the operating profits of a particular firm, those gains and losses would be distributed
across management teams. However the composition of managerial teams changes as
trade costs are reduced. Within a particular matching regime globalization leads to
matches which are more positively assorted. Furthermore, if trade induces a change
in matching behavior, a new regime emerges in which all managers prefer higher
skilled partners. In either case management teams form between managers with
more similar skills. As a result within firm wage inequality falls. The impact of
trade on the income distribution described here, with higher wage inequality across

firms and skill levels within industries but less inequality within firms, is consistent

with Dunne et al. (2004).

72

 

10 Conclusion

Worker behavior has far reaching consequences for production and labor market out-
comes in general equilibrium. The choices of laborers to provide eflort shape firm
organizational design and lead to unemployment. The decision of managers to match
is a key determinant of industry organization. With self-selection of firms into export
markets, endogenous formation of management teams can be an important avenue
for trade adjustment.

A reduction in transportation costs enlarges markets for only those firms produc-
tive enough overcome trade costs. As a result worker preferences for job type become
secondary to securing export status. Even the managers who have no hope of en-
gaging foreign consumers place less value on obtaining a particular job type, because
the alternative may be unemployment.

Modeling worker behavior is challenging technically, but the implications of trade
exposure for firms and workers may run opposite. Traditionally trade is thought
to cause agents to lean down and become more competitive. For firms this may
mean paring down the scope of activities that take place with its boundaries. For
workers this means dropping low ability partners, leading to better performing teams.
The partial incentive of firms to specialize may be eclipsed by improvements in team

formation.

73

Chapter 2 Appendices

Appendix A-Task Assignment of Heterogeneous Managers

The optimal strategy of a firm that hires mangers with two different skill
levels is to assign the more skilled manager to the task that uses her skill most in-
tensively. The function of each manager is to improve labor productivity in the
performance of a specific production task. So the intensity with which a managers
skills are used depend on both the increase in each laborer’s efficiency in performing
the requisite task and the amount of labor benefiting from skilled oversight. I define
the more skill intensive task to be the one that has the higher percentage increase
in labor productivity from additional skill, weighted by the unit labor requirement.
That is, the assembly task is more skill intensive for a firm that produces N vari-
eties of intermediates, with an average requirement of N efficiency units of labor for

modification activities, if

1 f'(s) N m’(s)

f (8) f(3) 771(3) ”1(3). (A.I)

 

 

 

 

Note that the modification task is more likely to be skill intensive at a firm that
produces a greater number of products (RHS is increasing in N). As intuition
suggests, a firm that produces a greater range of products will devote more labor to
modification activities. So, even if the modification task is relatively easy (gt/(13
is low) there may be a large amount of labor that benefits from managerial skill.
Another key feature of condition A.1 is that given the skill of each manager, product
market characteristics influence task assignment; the reason being that N is chosen
endogenously. As firms change their product scope and scale the ranking of the skill
intensity of each task might reverse. Therefore a manager may be reassigned to
different tasks when her employer adjusts its scope, even when the skill of her partner

remains constant.

74

Given this definition of skill intensity it still remains to be shown that the optimal
strategy of a firm is to assign the more able manager to the skill intensive task. To
do this I will show that operating profits increase more from a marginal improvement
in the skill of the manager assigned to the skill intensive task. Without loss of
generality assume that the assembly task is more skill intensive given firm scope; this
is the condition in Al.

The operating profits of a firm that hires two managers of Skill 3 are 7r (3,3) =
[ 11W”) [p(n) — wl (n)] :1:(n)dn. Exporting profits are omitted without effect. After
substituting the optimal price charged by firms and consumer demand, the increase

in profits from a marginal increase in the skill of the assembly manager is

 

 

9 —1 I
n 1 (EL—1 f (8)er (A.2)

"2(3’3’ : l C(f’y’wm IW+f(s) f(s)2

and the increase in operating profits from a marginally more skilled modification

manager is

 

~ —1 /
7r1(s,s)= / C(P,Y)wy€—1 (n + 1(971 Mdn. (A.3)

Firms will assign the more skilled worker to the skill intensive task (assembly task
by assumption) if doing so generates more profits. Averaging across all product lines

the criterion is

 

 

 

9
-—+ 6 N l m—l f’(3)
C P (119:1
( ’Y’ Im<s>+f(s) as)? >
9
6 N 1 F1" m' (3)]?
C wit—1 _
(P’Y) [m(3) + f(s):l m(s)2

 

 

 

 

asp

Appendix B-Equilibrium in a Median Matching Regime

A matching equilibrium occurs in a median matching regime when entry ((D1) is
rational and the median manager’s incentive compatibility constraint (4)2) is satisfied.
The equilibrium conditions are

(I31 E ex (—)-—btl—I(SL,Sjy1)dt F=0

(1’2 5 Wn “(511,50— Wf(SLaSM)=O

First, the implicit function theorem verifies that both conditions are downward

. . eel/as ‘ sag/as“
slopmg, — 081/651 < 0 and — 64>2/65L

and (D2 is unique only if one condition is everywhere steeper than the other. I will

< 0. Then the equilibrium defined by (1)1

show that in always more steeply sloped.

From Appendix A we know that

3‘1’1/3SL 7r1 (5L, SM)
—————=——————>—1 Bi
5‘1’1/85M 7r2 (SL, SM) ( )

Now substituting the managerial compensation function into condition (1)2 we obtain

1
(1’2 = 5 {7r (0,551) + 7r(51.1551) - ”(151.0”

- - 2{W(S MsO )+ T (81,13) — 71 (0,8)}. (B2)

76

and using the implicit function theorem to derive the slope of (1)2 we have

_ 3‘1’2/BSL ___ —I7T1(5L,SM) _- ”1(SL10)I _ .
022/3551 7T2 (0,551) + 7T2 (51,,le — ”1(35110) — 7r1 (SM: 5)

 

(B.3)

From 8.1, (1)1 is every where more steeply sloped than (1)2 only if the equation in

B2 is greater than —1, which is easily verified.

[”1 (513,531) — 7T1 (51.0)] +
[”2 (SL1 SM) - 7r2 (0,551)] +

[7T1 (SME) — 7r] (S

J.

,0)] >0.

Q.E.D.

77

Notes
15JEL Classifications: F16, L23, J21

16The term "partial-partial equilibrium" was coined by Rothschild (1973) as quoted
by Davidson and Woodbury (2002)

17Davidson, Matusz and Shevchenko (forthcoming) contains a similar feature where
heterogenity obtains from endogenous technology choices and exogenous worker—firm
matches. Also in Yeaple (2005) heterogenity is the result of exogenous skill differences
and endogenous technology choice.

18Production requires at least one manager to be hired. A single manager can apply
her skills to only one production activity. In the absense of a manager specifically
assigned to either task each laborer contributes his single efficiency unit of labor, i.e.
m(0) = f(0) = 1.

19See the appendix for a discussion of skill intensity of the tasks.

20As will be shown, firms will always recruit managers of different skill in equilib-
rium.

21Firms cannot strategically choose scope or price to attract a particular manage-
ment team. Free entry means that managers who are not working for firms selecting
price and scope based on (23) and (24) could be poached by entering firms that can
offer better compensation.

22This is not the same condtion as supermodularity of the profit function, even
though it is a direct result of it.

23For a discussion of matching regimes see Legros and Newman (2002) and (2007).

24I assume an equal measure of workers on either side of the median, each including
a median—skilled worker.

25Firm destruction leads to labor/ firm break up. Labor takes this probability
into account when making the decision whether or not to shirk. See the asset value

equations for labor in the previous section.

78

26Unemployment of managers is ignored as they are small relative to the entire

workforce. The set of managers who are not employed is determind endogensously
SL

and is given by / )1ch (s) .

0
2‘ For managers with the same cardinal ability the ordering is arbitrary.

79

 

 

 

 

, Operating

: profits- I Operating
: domestic : profits-

: sales : exports

l l

L A I \

N Z NEX n

Figure 2.1: Firm Product Scope and Extensive Export Margin

Skill of manager

 

 

 

with better
job type
S
Indifference
of Median
Entry
$ Skill of
51 manager

with low job
type

Figure 2.2: Determination of Employed Managers and Task Assignments

80

    

 

 

r-—--—--------

 

SR 5
Figure 2.3: Labor Market Equilibrium

lndifferenc
e of
Median

 

 

 

 

 

Figure 2.4: Effects of Trade Liberalization

81

11..
.....
.0

  

......
.19 O
.......
.0
.
.I
e‘.
.u

.o
e
.-
o
.e
-

  

r - m 5‘
sl SM

\
Y Y
Low Skill Intensity High Skill Intensity

Kat

 

Figure 2.5: Adjustments in Matching Outcomes within 3 Median Matching
Regime

82

Chapter?»
HOV and the Distributions of Factor Endowments

ABSTRACT: The shape of the distribution of labor endowments impacts
aggregate productivity when markets fail to organize labor effectively.
Variation in the level of dispersion in labor endowments across countries
lead to Ricardian productivity differences. These productivity difl'erences
impact the pattern of comparative advantage that arises from relative fac-
tor supplies. Using information about the overall shape of labor endow-
ments, rather than just cumulative levels, improves the ability of the HOV
model to predict the pattern of world factor trade. Countries export their
abundant factors as long as they can organize labor effectively. However,
estimating unexplained international productivity differences better ac-
counts for the volume of world factor trade; a result that could possibly
be due to attenuation and omitted variable biases derived from estimating

the shape of labor endowments.

11 Introduction

Heterogeneity, or diversity, in endowments influences aggregate productivity when
labor fails to organize effectively. In countries with diffuse distributions of labor
ability the cost of poor organization can be severe. An endowment with relatively
more workers with different levels of ability increases the potential for poor matching
and productivity losses. As a result countries with relatively large supplies of labor
may not posses comparative advantage in labor intensive goods when high levels of
dispersion erode productivity. If all countries have inherent problems organizing
labor the pattern of comparative advantage that arises is determined by the entire

shape of labor endowments, rather than just the cumulative mass of labor which

83

reside across borders.

I present a simple model with complemetarities between labor ability in the pro-
duction process so that an allocation of labor into teams with self—matching is the
most productive. That is, all teams should be comprised of workers with identical
ability. The production process is divided into two labor tasks, one more difficult
than the other. Performing the more difficult task is more important to the produc-
tion process. As team members negotiate over wages after production, the worker
who performed the more difficult task is in a stronger bargaining position, and thus
earns a discretely higher wage. Laborers pursue the wages guaranteed by better
task assignments by sacrificing match quality. Every worker is willing to accept
marginally less skilled partners for discretely higher wages associated with good as-
signments. The behavior of individual workers causes the labor matching market to
fail to deliver the most productive allocation in all countries. Productivity differences
across countries and the pattern of comparative advantage depend on the severity of
the matching market failure.

Greater dispersion in labor endowments creates the potential for large productiv-
ity losses; the realization of such losses is dependant on the vigor with which labor
pursues good task assignments. I derive two types of results that predict the impact
of dispersion on total factor productivity. First, if preferences for particular assign-
ments are very strong (i.e. wages differ significantly across tasks) then very poor
matches will be consummated. As a consequence, countries with larger amounts
of dispersion will exhibit lower productivity. I call this the Matching Outcome Ef-
fect. Consider an example where the production of T—shirts requires one worker to
supervise production and a second worker to advertise the shirts for sale to retailers.
Suppose that the production manager is more vital to the operation. All else equal
workers prefer to be hired as production managers, even if that means being matched

with a slightly less skilled advertiser. In countries that have relatively more high

84

skilled production managers and relatively more low skilled advertisers, aggregate
productivity will be lower. There will be too many workers chasing the benefits of
the good task assignments instead of productive matches.

The second prediction concerns individual matching behavior when the workers
do not favor task assignments strongly over quality partners. Again in countries
with high levels of dispersion there is greater potential for large mismatches. But, if
preferences for job types are relatively weak then individuals are not willing to accept
very poor matches. In this case workers prefer to be part of the best team rather than
be the star of a mediocre team. I refer to this as the Matching Regime Effect. Using
the example of production managers and advertisers, there may be some workers who
can find employment as production managers but only by matching with very poor
advertisers. In that case the production managers is entitled to a larger share of a
very small amount of profit. Instead it might be optimal to seek employment as an
advertiser with a more profitable firm.

These seeming contradictory implications of dispersion hinge in the relative ben-
efits of task assignments and potential match quality. I find that in those countries
with relatively low levels of dispersion the first effect dominates. Higher dispersion
erodes average factor productivity in countries with still relatively tight endowments
of labor ability. Among countries with very high levels of dispersion, those with
most heterogeneity exhibit the highest productivity as the Matching Regime Effect
dominates. Among the possible shapes of labor endowments the optimal level of
dispersion is zero, yet those countries with already high levels of dispersion may be
willing allow human capital accumulation to be concentrated among a small class of
workers as doing so would increase their productivity.

With the estimated impact of dispersion on productivity I am able to estimate
unit factor requirements across countries. Using trade and production data from the

OECD STAN database for 23 countries I measure world factor trade accounting for

85

—.., ~“

the different production technologies implied by the different shapes of endowments.
Information on the distributions of labor ability across countries are derived from
the Barro and Lee (2000) CID database on education attainment. I find that the
productivity effects of dispersion explain much of the observed deviations from the
HOV prediction. That is to say, countries export their abundant factors, as long as
they can organize labor effectively. Furthermore I find that information about the
shape of endowments can describe world factor trade patterns just as well as esti-
mated unexplained productivity differences, i.e. estimated Hicks-neutral technology
differences. Information about the shape of labor endowments has more difficultly
explaining factor trade volumes, although this result could be an artifact of statistical
biases that arises because the shape of endowments are measured imperfectly, and
features such as skewness are omitted.

Others have suggested that the problem of organizing labor effectively can ex-
plain much of international differences in productivity. and trade patterns. Clark
and Feenstra (2003) find that world trade during the period between 1910 and 1990
is best explained by differences in countries’ abilities to use labor and technologies ef-
fectively. They argue that easier transmission of technologies and information made
the best technologies more readily available the world over, but some countries failed
to absorb new technologies as well as others. While Clark and Feenstra infer from
trade patterns expected in an HOV environment that differences in the effectiveness
of labor are the responsible for cross-country productivity differences, I combine in-
formation about both trade and labor endowments to establish a causal link between
the organization of labor and aggregate productivity. Adler (2009) demonstrates that
even small deviations from optimal matching between firms and workers can lead to
large reductions in aggregate productivity. He cites matching frictions and crony
capitalism as reasons that matching markets may fail to deliver the most productive

allocation and explain international differences in TE P. Li (2001) argues that while

86

 

long-run productivity growth can only be explained by technological innovation, the
cross-section of international productivity differences are largely due to differences in
the organization and effectiveness of domestic labor forces. He shows that growth
among Chinese factories between 1980 and 1991 is best explained by better organi-
zation of labor to tasks and a greater amount of labor effort.

International trade theory has recently begun to explore the role that features of
factor distributions, other than aggregate supply, have on trade patterns. Grossman
and Maggi (2000) find that the degree of heterogeneity across countries can inde—
pendently grant comparative advantage in certain sectors. Countries with homoge—
neous populations specialize in goods with complemetarities in production, and di-
verse countries specialize in goods that reward individual talent. Similarly Bougheas
and Riezman show that differences the distribution of human capital leads to trade
between countries with similar aggregate endowments. They focus on the irnpli—
cations of trade based on the shapes of distributions of endowments has on income
inequality. In Grossman (2004) imperfect labor contracts provide an avenue for the
degree of heterogeneity to influence the pattern of comparative advantage. All of
these models consider trade between countries with similar aggregate endowments,
abstracting from potential interaction between diversity and aggregate supply. Ohn-
sorge and Trefler (2007) consider labor who differ along two dimensions, rather than
a single attribute such as ability. They provide an excellent analysis of how the
joint distribution of worker capacities influences trade patterns and highlight the
importance of the cross-correlation between different worker attributes. However
they abstract from the impact that variation of individual attributes on international
trade patterns28. Here my goal is provide an examination of how aggregate supply
and the amount of diversity jointly confer comparative advantage, demonstrating the
relevance of the Heckscher-Ohlin model in a world with heterogeneity.

In Davidson, Martin and Matusz (1999) the severity of labor market failures de-

87

termines the pattern of comparative advantage across countries. Search frictions vary
across countries and industries so that countries specialize in producing in industries
that reflect their relative efficiency of organizing labor during production. Cunat
and Melitz (2007) look to labor market institutions and the degree of flexibility in
the labor market to determine the pattern of trade. I introduce a market failure that
influences the allocation of labor that is common to all countries and industries. The
pattern of comparative advantage is driven by relative factor supplies and the shape
of labor endowments, rather than the structure of the labor market.

The most relevant theoretical framework to this analysis is found in Costinot
(2009). He provides sufficient conditions on aggregate production functions for factor
abundance to translate into comparative advantage. The key is log-supermodularity:
it must be that relatively more of a particular factor used in production implies rel-
atively more output. The matching environment here provides micro-foundations
for an aggregate production function based on the formation of teams. His analysis
provides a generalized interpretation of my theoretical predictions and empirical find-
ings. If preferences for particular task assignments are strong, then the aggregate
production function is not log-supermodular. As a result factor abundance does not
necessarily confer comparative advantage. The microeconomic explanation being
that poor matches are formed and productivity suffers.

There is of course a long literature which scrutinizes the HOV model theoretically
and empirically, uncovering paradoxes and mysteries along the way. The initial
wave of research built statistical techniques for examining the validity of the HOV
prediction that countries export their abundant factors, each rejecting the model in
turn. See Leontief (1953), Bowen et al. (1987), Maskus (1985) among many others.
Trefler (1995) was the first to show that the volume of predicted trade is far below
predicted levels given relative factor endowment. In a recent contribution Trefler and

Zhu (2006) define the factor content of trade in a manner that is both Vanek relevant

88

and consistent with trade in intermediates in and international technology differences.
Trefler and Zhu (2000) argues convincingly that the HOV model is still valuable given
the need to account for productivity differences, as suggested by 'I’refler (1993) and
Davis and Weinstein (2001).

The next section describes world endowments, production and the trading envi-
ronment. In section 3 I establish that domestic matching markets necessarily fail
when a certain type of job provides a discretely higher wage, all else equal. Section
4 relates the level of dispersion to the costs of market failures in terms of aggregate
productivity. I then empirically evaluate the role that dispersion plays in the deter-
mining world factor trade. Section 5 describes the data on production technologies,
world trade, and the shape of endowments. Section 6 estimates productivity dif-
ferences across countries and shows that dispersion is able to explain much of the
international differences in TF P. Also, the shape of the labor endowments is shown

to strengthen HOV predictions of world factor trade. Section 7 concludes.

12 Model

12. 1 Production

The world economy is comprised of many countries labeled 1...C, which each use labor
and capital services to produce output in several industries labeled 1...N. Consumers
in all countries have identical homothetic preferences. With free trade in competitive
markets every country faces the same prices for each sector given by p;. Within
each industry labor services, I, and intermediate capital goods, k, are combined to
manufacture output according to lfiikl—fii for i = 1...N. Production in any industry
requires both labor and capital (i.e. 6,- E (0, 1) Vi). Furthermore production benefits
from (1) the cooperation of labor in the completion of specific tasks and (2) the

specificity of capital to the skills of workers. Though self employment is possible,

89

the complementarities that manifest through division of labor allow for more eflicient
production.

The Vanek prediction is that countries will export a factor if they are abundant in
that factor relative to the world endowment. With team production of labor services
and intermediate capital goods, the amount of each factor a country uses in production
of per unit of output also depends on the organization heterogeneous workers into
matches. I will discuss raw factor endowments first and then the organization of
teams. Capital is an ex ante homogeneous and divisible factor that can be modified to
suit the needs of any industry, and the skills of any worker. Total capital endowments
KC vary across countries. Each country’s endowment of labor is populated by a mass
LC of heterogeneous individuals who differ according to their ability, a, in performing
labor tasks. The distribution of labor ability, given by G6 (a) over the interval [g, a]
for country c, can vary across countries in two ways. Countries may have different
different levels of human capital per capita. Also countries can vary according to
their level of dispersion about the mean according to the following definition.

Definition 1 Country i is said to have a more diffuse distribution of

. G-
human capital than country j {both with mean ability ii) if gig); < 5% for
2 J

G,(a) > Ella)
02(0') Gj(a’)
Variation in the level of dispersion in labor endowments across countries satisfies the

 

a>a’>’dand for’d>a'>a.
monotone likelihood ratio property about the mean. A more dispersed endowment
of labor is characterized by relatively more labor with extreme levels of skill above
and below the mean. This is a stronger condition that stochastic dominance, as
discussed in Costinot and Vogel (2009), because it describes the relative abundance
of each level of ability, rather than just the cumulative degree of abundance across
abilities.

Team production divides labor services into two distinct tasks with different skill

intensity. Laborers with ability a1 and a2 combine their effort according to the

90

production function l(a1,a2) = algal—0 + a? + aé—o with 0 6 6,1). When 61 is
close to 1, a single member of the team carries a large burden during production,
while her partner contributes little. As 6 approaches % production uses each team
member more equally. Although the production framework for labor services implies
a degree of cooperation between worker, the model is meant to apply generally to
circumstances where workers perform their respective tasks in isolation. Consider an
example of the retail sale of T—shirts. There is no reason to think that workers who
manufacture shirts must interact with advertisers, however they benefit from each
others’ efforts. Team production need not be interpreted as production by a single
economic agent such as a firm. Rather laborers that perform each task should be
considered independent utility maximizers who exchange their tasks in a market.

Capital endowments are comprised of raw materials that are ex ante homoge-
neous. To be used in production capital must be transformed into intermediates
which are relevant to the skills of each labor team. Forging capital into interme-
diates is costly; these costs are larger for teams comprised of workers with different
levels of ability. Only one design of intermediates is necessary for homogeneous
teams. If teammates have different abilities, then capital must be modified further
so that both workers can take full advantage. Team members with large differences
in their abilities require use more units of raw capital to manufacture relevant in-
termediates. To be explicit, if one unit of capital is allocated to a team comprised
of workers a1 and a2 then the amount of intermediate capital goods available for
production is k = 1 — r |a1 — a2| .

This style of team production has several important features. First, production at
the industry level exhibits constant returns to skill. For any industry if the amount of
capital employed were doubled and the exact number and composition of labor teams
were duplicated, the industry would double its output. The second crucial feature

of production is that industry output depends on not only the aggregate amount of

91

 

labor ability employed in each industry; the matching of workers according to their
abilities is an important determinant of productivity. Complementarities in worker
skill and the need for intermediate capital goods that are relevant to the skills of
workers imply that productivity is the greatest when all workers self-match; that is
the labor market is perfectly segregated according to skill.

Third, the total supply of labor services by any pair of workers depends on the task
to which each worker is assigned. If matches form between heterogeneous agents29,
then output is maximized when the most able of a pair of workers is assigned to the
skill intensive task. Fourth, the design of intermediate goods to be specific to the
skills of the workers using them is not meant to imply any sort of bias30. Intermediate
capital goods are generated at a disaggregated level based on the skills of individual
teams rather than the labor market in general.

Based on this (admittedly stylized) production function countries will exhibit
greater productivity when domestic markets allocate relatively skilled workers to dif-
ficult tasks, and similarly skilled laborers into teams. Poor matching outcomes can
erode both labor and capital productivity31. Thus the avenue for skill dispersion
to influence the factor content of trade to be examined here is the impact dispersion

has on the allocation of domestic workers into matches and to tasks. The matching

behavior of workers is driven by the desire to earn high wages.

12.2 Labor Wages

Total production is determined by the composition of teams and task assignments of
labor. As a result wages are a function of (1) a worker’s own ability, (2) partner’s
ability, and (3) task assignment. Competitive markets, and free trade equalize the
price of labor services, or, across countries32. The total payments for labor services
must further be divided among the pair of workers. I use the Shapley Value to

determine the ez' post division of surplus as in Hart and Moore (1990) and Acemoglu,

92

Antras and Helpman (2007). Since payments are made after production occurs, no
laborer has a claim to the surplus earned by other teams. During negotiation team
members first have a claim to the surplus generated solely by their own actions, and
then must divide an surplus that arose from cooperation. Therefore laborers earn
the average of their marginal contribution to the production of labor services.

Labor with skill level a, performing a task designated by 6, and matched with a
worker of ability m (a) will earn

w(a, m (a) a 6) = $0106 + $01 [a6m(a)1—6 + (a6 + m (a)1_0) -— m(a)1_9]

The first term represents the marginal contribution of a worker with ability a to
production when working alone and the second term is worker a’s marginal contri-
bution to the team when paired with a laborer with ability m (a). The term % is

included to average the two terms. Simplifying provides labor wages expressed as
1
w(h, m (h) , 9) = wa‘9 + iwa0m(a)1_6 (36)

This determination of labor wages exhibits several intuitive properties. First, all
else equal a laborer’s wage is increasing in her own skill level because higher skill
leads to more production. Second, a laborer’s wage is increasing continuously in the
ability of her partner. A better partner leads to greater output of total labor services
from the team, and a greater amount of surplus to be divided. Third wages are
discretely higher when assigned to perform the skill intensive task. A worker who
is relatively important in the production process contributes more on average, and
so extracts more surplus ex post. Fourth, wages are increasing in the market price
for labor services to, since each worker receives a portion of the total surplus to labor
services that is to be divided. Larger payments for labor services result in higher

wages for both members of the team.

93

The last feature of wages is that by assuming a structured division of surplus
among workers I have assumed the labor market environment to be one of non—
transferable utility (NTU). Workers cannot make side payments to each other. The
next section discusses the matching of laborers and task assignments. Assuming NTU
is not without consequence for the allocation of labor to tasks and into matches.

It is important to keep in mind to style of team production that motivates the
assumptions about production and wage bargaining. Although all goods require a
pair of specific labor tasks to be completed, there is no reason to think that workers
interact, cooperate, are part of a single institution (i.e. firm), or even know the
identity of one another. They can simply ofier their services, "meet" in a market
setting, join with capital and engage in production. The dislocation of laborers
geographically within borders, or practically during production reduce the likelihood
of side payments. Thus the contractual obligation of laborers to divide surplus
according to the Shapley Value is taken as a primitive of the model.

The fact that labor wages increase in ability, partner’s ability, the price of labor
services, and skill intensity task assignments all seem like plausible relationships.
However there is a subtle distinction to draw between the manner by which each
component influences wages. Being paired with a high ability worker increases the
gross amount of surplus to be divided among a team. So wages are increasing in
m (a) and to because they increase the total size of the pie to which a worker has a
partial claim.

On the other hand a worker being more skilled herself, or having to perform
the more difficult task, entitles her to a greater share of the payments to the team.
Greater ability and good jobs increase the size of the piece of the pie awarded. The
next section describes the behavior of workers. This distinction between wage in-
creases via entitlement to a share of a large sum of monies versus a larger share of the

monies divided among the team will be crucial to the endogenous formation of teams.

94

Workers face a trade-off between obtaining good task assignments and obtaining good
matches. A last point before describing the allocation of labor is that even though
production with "self-employment" is possible wages are always higher when paired
with another worker because of complementarities between skill in production and

the division of surplus between team members.

13 Allocation of Labor

Labor is fully mobile across industries, can perform any and all tasks in the economy
(albeit with differing success), and form matches voluntarily. Labor services are
divisible so that a team could potentially "be employed", or sell their services, in
multiple sectors. Given the manner of wage negotiations outlined above, all else
equal, each laborer would prefer to match with the highest skill partner, and perform
the task that makes the most use of her abilities. However such desires are not
feasible. As all workers compete for the best jobs with the best coworkers, many
will be crowded out. The allocation of labor has three components (1) the set of
workers performing high or low skill intensive tasks, (2) the specific matches between

partners, and (3) the allocation of labor across sectors.

13. 1 Task Assignment

With heterogeneous labor the assignment of workers across tasks has important con-
sequences for total output. Labor services are produced more efficiently when the
most able worker in a match is assigned the more difficult task. When making
matching decisions, utility maximizing agents force the allocation of heterogeneous
team members to tasks to be the most productive; otherwise they would seek optimal
matches elsewhere.

I

To see this consrder a team comprised of labor w1th abrllties a' and a w1th a'

95

< a’ ’ . Suppose worker a’ ' is assigned to the relatively easy task (1 — 6). Now consider
a worker with ability a* E (a,, a”). If worker a* is matched with a worker of ability
greater than a’ ’ then there is potential to for a” to raid the team as she can offer a
better match, and no worse task assignment to the partner of a* . Both opportunities
would benefit the partner of a* as wages are increasing in partner’s ability and task
assignment.

If a* is matched with a worker of ability less than a’ ’ there is potential to for a”
to raid the team as she can offer a better match, and no worse task assignment to
a*. Again both would bring higher wages to a*, and so the raid by a” would be
successful. In either case raiding would be optimal since a” would obtain a better
partner, and thus a better wage. Matches with inefficient task assignments are not
stable because the more able member of the team could always find a better match

elsewhere. Therefore the following result is obtained.

Proposition 10 With continuum of labor ability, if teams are comprised of heteroge—
neous laborers, matches are stable only if the more able member of the team performs

the more skill intensive task ( denoted 6 )

Laborers face a trade-off between task assignment and match quality. Proposition
1 tells us that the only way to guarantee a better task assignment is to accept a match
with a partner who has lower ability. Each laborer must weigh the benefits from
efficient production against enhanced bargaining power when considering potential
matches. This result has limited scope in that it only describes task assignment
between a specific pair of workers, rather than types of labor in each country assigned
to each task in equilibrium. At this point all we know is that relatively able labor

will perform more difficult task in a stable environment with heterogeneous matches.

96

' f

 

13.2 Matching Outcomes

Matching between agents in each industry occurs endogenously, without frictions or
costs. Holding task assignments fixed, the wages of all labor are increasing in the
ability of their partners. To be more specific the payoff functions for laborers in (1) are
supermodular. At an aggregate level labor can be divided into two groups that must
have equal measure: workers willing to accept a low skill task, and the workers who
obtain high skill intensive task assignments. Supermodularity of the wage function
(wage increasing in partner’s ability) implies that the pattern of matching between
these two groups will be positive assortative matching33 (PAM). Competition for
matches leads high ability workers to match with relatively high ability workers, and
low types to match with relatively low types.

This is a one-sided matching context, with labor forming teams based on a single
characteristic, ability. However it can be useful to think of it as a two—sided matching
problem occurring in two stages. First, laborers decide if they are willing to accept
a poor task assignment in anticipation of their match in the next stage. Second,
matches form based on the abilities of workers in each group. Without knowing
the exact distribution of ability in each country we cannot derive the equilibrium
matching pattern in general. This is because we cannot describe the sets of workers
within each country willing to accept poor task assignments. What can be inferred
from the complementarity of worker abilities in wages is that once the sets of labor
willing to be assigned to each task are determined, in the second stage workers will
match positively.

Even though an equilibrium in the first stage cannot be derived for arbitrary dis-
tributions there are still regularity conditions that must be satisfied for an equilibrium
to exist. Such restrictions provide at least some insight about how workers decide
which type of task to pursue. First, proposition 1 guarantees that for any pair of

workers the most able member of the pair will receive the better task assignment. The

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most able worker in each country will always perform difficult tasks and visa versa
for the least able member in each country. Second, because team production always
yields higher wages than self employment, all production occurs in teams. Therefore
the measure of workers who choose to perform either task must have equal measure.
Third, the properties of the wage function imply the second stage allocation of labor
into matches will be positively assorted. Given the many potential matching regimes
that can arise in the first stage, it is worthwhile to describe a few examples and the

conditions under which they may arise.

13.2.1 Possible Matching Regimes

The most extreme form of positive assortative matching is perfect segregation, or self—
matching. In the perfect segregation matching regime nearly every laborer would
be paired with one who has the same skill level34. Complementarity in production
implies that self-matching is the matching regime that leads the greatest aggregate
productivity. However perfect segregation cannot arise in equilibrium in the present
context because laborers have strict preferences for a particular job type because of
the improved bargaining position it guarantees. Consider any homogeneous match
in a perfectly segregated matching regime. The laborer assigned to the low skill
task could earn a discretely higher wage by matching with a marginally less skilled
partner because doing so guarantees a better task assignment (Proposition 1). The
continuity of labor abilities ensures there is a marginally less skilled worker performing
the low skill task. Moreover, a self-matched worker assigned arbitrarily to the low
skill task could obtain a better wage by matching with a higher skilled partner, while
still performing the low skill task. With self-matching across all levels of ability,
labor who receive poor task assignments will always be able to find either better task
assignments or marginally better partners elsewhere. Thus we have the following

result:

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Proposition 11 If there is a continuum of abilities in each country, the allocation of

labor into matches will be such that all matches form between heterogeneous laborers.

Propositions 1 and 2 point to the heart of the analysis here. Because of the way
labor contracts are written in each country, all individuals are willing to forgo the
labor allocation which is most productive at the aggregate level in order to secure
private benefits. The matching market fails to deliver the optimal outcome because
labor wages only give partial weight to total production. The severity of this market
failure in terms of aggregate productivity is determined by how strongly labor will
pursue the good jobs. Put differently, the potential productivity losses are greater
when labor are willing and able to find poor matches.

Even though the most productive allocation can never be reached, some countries
may be able to operate closer to the productivity frontier than others. Total produc-
tion receives at least partial weight in the matching behavior of labor. At some point
the loss in productivity losses of poor match quality becomes so great that labor may
begin to accept less skill intensive positions. To see this formally consider the change
in wages a worker receives for matching with a less able partner in order to obtain a
better task assignment. Define é—E’é—A as the private benefit of pursuing a better task
assignment.

Aw(-)_ , ~ _ _
A6 —u(a,m(a),6) w(a,rn(a),1 6) (37)

 

where 717(2) is the match that a worker of skill at obtains if he finds a job performing
the skill intensive task. A worker would only choose to reject a good match and
take high skill task assignment if this expression were positive. Substituting the
expression for wages into (37) yields

Aw ()
A6

 

I ~ 1—6 1
= wag + Ewa6m(a) J — [coal—6 -+— Ewm(a)6a1_6 (38)

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EFI

..
_-.-..

Clearly the gain from switching to a better task assignment is smaller as the ability
of the match one obtains by switching is lower; —d AEé—l/dmm) < 0. As match
quality deteriorates 3375—2 will eventually become negative, and labor will no longer
reject good matches for the sake of good task assignments. As more more groups of
abilities experience negative values of 33%) the matching regime will be characterized
by more segregation.

By way of example consider a worker who has the choice of being hired as a
production manager, the skill intensive task assignment, but only by pairing with a
low ability advertiser. The performance of the advertiser could be so poor that the
production manager would rather given up her job and match with a better partner,
even if that means becoming a advertising executive herself.

The opposite extreme of perfect segregation is a pattern called median matching.
This occurs when all labor in the industry are willing to sacrifice match quality to
obtain good task assignments. That is, better task assignments lead to higher wages
for all potential matches (%2 > 0 for all a). More intense competition for task
assignments comes at the cost of match quality. Thus median matching is the least
productive allocation of labor into matches. In equilibrium only half of laborers
can actually obtain the better of the two assignments, as the measure of workers
performing either task must be equal. Proposition 1 dictates that those above the
median skill level will perform the more difficult tasks and visa versa. The matching
regime will still exhibit positive assortative matching between those assigned to either
task. Hence labor will match positively across the median. The most able laborer in
each country will match with the most able person willing to accept the low skill task
assignment: this is the median skilled laborer as everyone at or below the median is
crowded out of high skill task by more able labor.

In the next section we will derive in impact of greater dispersion in a country’s

skill endowment on match quality. Dispersion influences matches in both stages of

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the matching game by first influencing the set of workers willing to accept each task
assignment, and second influencing the pair of abilities that form matches holding
labor assignments to tasks fixed. I will refer to the impact of dispersion on the range
of workers assigned to each task in the first stage as the Matching Regime Effect and
the impact of dispersion on the specific pair of abilities that form teams in the second

stage as the Matching Outcome Efiect.

13.3 Allocation across Industries

Labor services are employed by all industries. The market for labor services clears
when there is zero excess demand (z;(w)) in all industries at price equal to w. The
last equilibrium condition that must be satisfied is full employment of labor services.
Note that this is not necessarily the same as full employment of labor; constant return
to scale in the production of labor services, and no barriers or frictions in the labor
market, ensure that full employment of labor will be obtained. Define I ( ) as an
indicator function that equals 1 if its argument is an laborer who obtains a skill
intensive task assignment and zero otherwise. The industry-level and country-level

equilibrium conditions are respectively

z,(w) = 0 for industries i = 1...N

LC = [1..- (a) (59%)1'6 + 59 + [(3)149

14 Distribution of Labor

Positive assortative matching is an ordinal mapping of labor performing either task
to one another. Aggregate productivity depends on the cardinal abilities of workers
who form matches. Therefore the overall distribution of labor ability has first—order

implications for productivity by either influencing the matching regime which arises

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in equilibrium or influencing the matching outcomes within a particular regime.

14.1 Dispersion & Matching Outcomes

Recall that dispersion as given in definition 1 is identical to imposing likelihood ratio
dominance about mean. In a country with a more diffuse distribution there are
increasingly more workers with abilities away from the mean. Consider any worker
with above average ability. In a country which has a more dispersed endowment
of labor there are relatively more workers with even greater ability. That is to say
relatively able labor who are native of countries with diffuse labor endowments face
more intense competition for the best matches. Holding task assignment fixed, each
laborer above the mean is ordered lower when ranked according to ability against
others performing the same task. Positive assortative matching then implies that
the matches obtained by above average workers in diffuse countries are less than or
equal to the quality of matches in countries with relatively tight labor endowments.
The implication for productivity is given in the following lemma.
Lemma 1 Holding task assignments fired, labor with above average ability will
form less productive matches in countries with more dispersed endowments of labor
The converse is true for abilities below the mean. For abilities below the mean
there are relatively more labor with even lower ability in countries with dispersed labor
endowments. These low skill agents could potentially be better off when competing
for matches in diffuse labor endowments. However better matches for low skill
workers results in lower productivity at the aggregate level; the gain in the match
quality of low ability workers limits the degree to which a diffuse country can exploit
complementarities in production or take advantage of abundant factor supplies.
Lemma 2 Holding task assignments fired, labor with below average ability form
less productive matches in countries with more dispersed endowments of labor

Both lemmas are made with the caveat that task assignments are held fixed. They

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only apply when the same groups of labor pursue each task assignment for various
levels of dispersion. Recall that workers pursue good task assignments as long as
9&2, the private benefit from doing so, is positive. If there are any workers on the
margin (9%? near zero) then dispersion may also shift the matching regime, as will be
discussed shortly. Proposition 2 ensures that all matches will form between workers of
different abilities because every worker is willing to sacrifice match quality at least to
a small degree. Lemmas one and two demonstrate that as long as labor still seek the
private benefits which accompany good jobs, their willingness to accept poor matches
has greater consequences in countries with more dispersed labor endowments.
Together lemmas 1 and 2 describe impact of dispersion of a country’s labor en-
dowment on the quality of matches. Relating matching outcomes to productivity

in an environment with complementarities between skill in both labor and capital

productivity, the following result is obtained.

Proposition 12 ( Matching Outcome Efiect} If the benefits of good task assignments
are large, then countries with greater dispersion in their labor endowment will exhibit

lower productivity in terms of factor usage.

14.2 Dispersion & Matching Regimes

Labor wages can be split into two components: half of wages are derived from in-
dividual contributions and bargaining power, and half are derived from the amount
of team production. While full weight is not given to team production erosion of
match quality can be severe enough to eclipse the benefits from better task assign-
ments. The private benefits of good task assignments decreases as match quality
worsens (recall that — défigi /dm(a) < 0). In countries with more diffuse labor en-
dowments, those with above average ability face more competition from above for
good matches. Competition for matches among relatively skilled workers reduces

the premium earned from good task assignments. Eventually the productivity losses

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may become severe enough that some skilled workers are willing to forgo better task
assignments and seek better partners.

Lemma 3 Labor with above average ability are more willing to accept high quality
matches over good task assignment in countries with dispersed labor endowments.
Even though workers who are relatively skilled have an advantage ex ante in securing
good jobs (Proposition 1), they may not choose to exercise that advantage when
competing in a matching market with diffuse supply of partners.

As high ability labor begin to accept poor task assignments, matching outcomes
of those with below average ability must also adjust. When relatively able workers
begin matching with even more able workers, they are unavailable as partners to the
relatively low skilled. On one hand, competition among those willing to perform low
skill task intensifies. On the other hand, opportunities to perform high skill tasks
become available as there must always be an equal measure of labor performing each
task. Both lead below average workers to pursue good task assignments. Those who
do so must match with labor of even lower ability for their partnerships to be stable
(Proposition 1). Responding to the behavior of relatively able workers, the impact
of dispersion on relatively low ability workers is summarized in Lemma 4.

Lemma 4 Labor with below average ability are more likely to obtain good task
assignments and form high quality matches in countries with dispersed labor endow-
ments.

From an individual perspective some skill levels may earn higher or lower wages in
countries with different levels of dispersion based on their specific matching outcome
and task assignments. But the emphasis here is on aggregate matching outcomes and
the consequences for productivity. Lemmas 3 and 4 indicate that greater levels of
high levels of dispersion diminish the benefits derived from having more negotiating
power and thus alter matching behavior. Stronger emphasis on team production leads

to more segregated matching patterns. When the patterns of task assignments differ

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across countries dispersed labor endowments have the following impact of aggregate

efficiency.

Proposition 13 ( Matching Regime Efiect} If dispersion alters the pattern of task as-
signments across countries, then countries with greater dispersion will exhibit greater

productivity in all sectors.

14.3 Discussion

Several partial results have been derived above and a discussion of them together is
prudent. First, proposition 1 demonstrates that worker preferences for specific job
types necessarily cause the matching market to fail to deliver the efficient outcome.
In the model laid out above preferences come from the inherent bargaining power
associated with each assignment. There are several other features of labor payments
that may distort the allocation of ability during production35. Information asymme-
tries may exist and one job type may come down on the better end of negotiations
when effort or productivity are not observed perfectly. Non-pecuniary benefits such
as health care plans, contract length, or organizational authority can influence pref-
erences over jobs. Certain professions, or positions within companies, may grant
better social status. In any event, certain benefits attached to only a faction of jobs
available inhibits the ability of the market to organize labor effectively.

With complementarities between worker abilities in production the severity of
failure in the matching market is measured by the degree of heterogeneity in matches.
Dispersion in labor endowments create the possibility of drastic productivity losses
because of the relatively larger shares of workers of different ability. That is, matching
outcomes have the potential to be worse in dispersed endowments. Proposition
3 demonstrates that when market failures are persistent (i.e. preferences for task

assignments are strong), countries with more diffuse distributions do indeed suffer in

terms of productivity. This result must be reconciled with the finding in Proposition 4

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which states that greater dispersion with a country provides incentives to labor in that
country to make decisions about task assignments which improve total productivity.

The two seemingly contradictory predictions influence productivity through dif-
ferent mechanisms. Whereas dispersion makes market failure more costly, dispersion
also makes severe market failures less likely to occur. Therefore it is an empirical
question whether or not dispersion in labor endowments influences total factor pro—
ductivity across countries or over which ranges dispersion it is detrimental / beneficial;

the next section tries to answer this question.

15 Data

The goal here is to provide a complete test of HOV predictions of the factor content of
trade accounting for the influence of skill dispersion in a country’s labor endowment.
In order to perform complete tests data on technology, trade and endowments are
needed from each country. These data come from the 2005 edition of the Organization
for Economic Cooperation and Development STAN database. Reported are labor
and capital usages, gross output, value added and bilateral trade data for 25 industries
in the manufacturing and non-manufacturing sectors. Observations are taken from
the year 1995 for 23 countries36. Although the coverage of this data set is quite
extensive, there are missing data problems for production and factor requirements in
many industries and countries. The data appendix describes the data set in more
detail and also the methodology used to impute missing observations.

Information on the distribution of skill in each country are from Barro and Lee
(2000) data set at the Center for International Development which reports educational
attainment levels across countries every 5 years. For the year 1995 the percentage
of the population over the age of 15, in each country, which attain one of four levels

of education are observed; the levels are No Schooling, Primary Attained, Secondary

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Attained, Higher than Secondary education attained. Note that these group are
mutually exclusive in that the percentage to the population with Secondary Attained
is the percentage whose maximum level of education is secondary school. These data
provide very detailed information about the composition of the labor force in each
country, yet still suffer two important limitations.

First, the mapping of education into human capital is not evident. It is not clear
which levels of education provide the most marketable skills to workers. Therefore
I will construct estimates of the labor endowment in each country (in terms of total
ability or total Human Capital Accumulation) under the assumptions of increasing,
decreasing and constant returns to education. The one restriction that I impose is
that all countries education systems yield the same returns from each level of ed-
ucation attained37. Specifically let N EC denote the percentage of the population
in country c which has no education. Similarly define PC, SC, BC as the percent-
ages of the population in country c which attained primary, secondary, and beyond
secondary education levels respectively. I normalize human capital endowments by
assuming that uneducated labor have zero human capital. Thus the total human

capital endowment per capita in country c is given by

HGAC 2 PC at (1) + SC >1: (2) + BC * (3) under Constant Returns
HCAC = PC * (12) + SC >1: (22) + BC =1: (32) under Increasing Returns

HCAC = PC * (\/I) + SC >1: (\/2) + BC * (\/3) under Decreasing Returns

A second gap in the data is that the levels of education are not observed by age
group. Were it the case that information about age were available the estimates
of human capital accumulation could be refined to include a degree of experience.
Higher levels of education concentrated among a young group in one country would

plausibly indicate a lower level of human capital accumulation than a country where

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the same percentage of workers have been educated, but also have the benefit of years
of experience. These two limitations notwithstanding, information on educational
attainment within each country shed light on the differences in the composition of
labor endowments across countries.

The last piece of information to be included in the estimates of factor productivity
and factor trade is the amount of dispersion in each country’s labor endowment. If
every individual in an economy were to attain the same level of education, then
each share of the population should have an equal share of the total human capital
endowment. For example, in a country with no dispersion in the distribution of ability
any 25% of the population should have 25% of the total human capital endowment.
The percentage of the population which completes each level of education are observed
and total human capital accumulation can be estimated. Therefore the level of
dispersion in each country can be represented by a pseudo-Gini coefficient. For each
level of educational attainment, I compute the difference between the equal share of
human capital and the actual amount of human capital accumulated by all workers
at or below each level of education. For example, dispersion in the labor endowment

of country c, under constant returns to education, is

gDC = {NEG * HCAC} + {(NEC + PC) at HCAC — [PC >1: (1)]} +

{(NEC + PC -I- SC) * HCAC — [PC a: (1) + SC at (2)]}

Measures of dispersion under increasing and decreasing returns are calculated in a
similar manner. The first term in braces represents the fact the in country c a per-
centage of workers N EC accumulated no human capital. Yet if the human capital
were equally divided among labor they would have accumulated N EC :1: H C'AC units.
Likewise the second term in braces demonstrates that if labor who received only pri—

mary education or less were to have an equal share of the human capital accumulated

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in country c they would have (N EC + PC) a: H GAG units. Instead labor with primary
education or less received only PC =1: (1) units with constant returns to education. The
third term in braces has an identical interpretation.

If all workers in a country attained the same level of education, say secondary,

then the measure of dispersion in that country would be given by
gDC = HGAC —— SC =1: (22) = SC * (22) — SC * (22) = 0.

Clearly the pseudo-Gini measure of skill dispersion is larger as different shares of
workers receive different levels of education. Table 3.1 reports the estimates of per

capita human accumulation and measures of dispersion for each country.

16 Empirics

Two types of statistical tests are necessary to evaluate the impact of dispersion of
labor endowments on the factor content of trade. As suggested by the Trefler (1993)
and Davis and Weinstein (2001) technology differences across countries are central
to factor content studies. The theoretical framework provided above describes how
dispersion influences productivity (i.e. technology) across countries when matching
markets fail to deliver efficient allocations. This is the first statistical test performed
below. Clearly, the modes of production across countries influence the factor content
of the goods they send abroad. The second set of tests examines whether or not
the degree of labor heterogeneity influences factor trade patterns in a manner con-
sistent with the benchmark HOV prediction. The link between factor supplies and
factor trade is tenuous at best. Additional information about endowments, such as
dispersion, allow a more precise line to be drawn between endowments and trade.
This section first provides evidence that Hicks-neutral technology differences ex-

ist between countries. Then the degree of labor heterogeneity is shown to explain

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much of these differences. The evidence suggests that matching outcomes are worse
in countries with high levels of dispersion, consistent with the notion that labor has
strong preferences for job types. Third, I construct technology matrices for each
country derived from their measured level of dispersion. Combined with bilateral
trade data, these technology matrices provide estimates of the world factor trade.
Next, observed factor trade and factor endowments are measured against HOV pre—
dictions. In the end I find that information about all features of the shape of labor

endowments together can tell much of the story of international trade flows.

16.1 Technology Differences and Dispersion

Let A be the common N x f matrix of factor requirements so that Aif is the amount
of factor f (labor or capital) needed to produce a single unit of output in industry i =
1...N. If all countries used the same technologies then we would observe A29 = E}
for all countries. Following Davis and Weinstein (2001) suppose that factor usages are
observed imperfectly and that such measurement error is distributed log—normal with
mean zero. Moreover, countries may use the commonly available technology with
differing levels of efficiency. If these productivity differences are Hicks-neutral, then
factor usages would differ proportionally from a common technology38. Accounting
for measurement error in each country across factors and industries, denoted as {SP
and productivity differences each country, given as OC, factor usages in country c are

centered around the common technology matrix A with elements Aif that satisfy
43 = ecAz'fiff

Technology differences OC and the common available technology can be estimated

in log form by running the following regression, with 60 = In 90, eff = 11155,, and

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Aif = lnA,f
ln A5,. = ac + A.” + cf, (39)

In order to estimate (39) a normalization is required. As is standard I use the
United States as the basis of comparison by setting 66 = 0 (equivalent to OC =
1). Also I weight each observation by the square root of the log of value added in
each industry to account for heteroscadasticity that arises because large sectors are
likely to be measured more precisely. Table 3.2 reports the estimates of technology
differences. To no surprise there is significant variation across countries. Belgium,
Canada, Finland, France, Netherlands, Norway, Sweden and the United States are
indistinguishable in terms of productivity and are more productive than every other
country. Korea is the least productive of the sample, requiring approximately of
six and a half times as much of each factor to produce the same amount of output.
Australia, Hungary and Poland also exhibiting severe productive deficiencies. .
Having established that international technology differences exist, the next step
is to relate the degree of heterogeneity, or dispersion, in labor endowments to overall
productivity. Rather than estimate country-fixed effects as in (39) we will use the
pseudo-Gini coefficients as measures of dispersion in labor endowments and human
capital accumulation per capital as a measure of average ability across countries. The
theoretical framework above does not specify a functional relationship between factor
requirements and dispersion. Furthermore, the theoretical characterization of disper-
sion hold average ability fixed. The impact of dispersion on technological efficiency,
controlling for the average level of ability, and using higher polynomials approximate

the impact of dispersion, can be estimated in reduced form by the following regression.
ln A3,. = BlgDc + 52 (gDC)2 + 63HCAC + 11,-, + (if, (40)
If preferences for good job types weigh heavily on labor behavior, then dispersion has

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an adverse effect on productivity. Evidence of strong preferences for jobs would be
positive coeflicients on the dispersion measures. The corresponding estimates of the
Matching Outcome Effect would be 61+ 2figgD > 0. While a high level of dispersion
raise the potential costs of failures in the matching market, it also makes them less
likely to occur. More efficient matching regimes may arise in countries with high
levels of dispersion. Estimates of the partial effect of dispersion would be less than
zero if the Matching Regime Effect dominated.

The theory fails to return sharp predictions characterizing the role that dispersion
plays. Both positive and negative estimates have explanations within the framework
above. Difficulty would only arise if no significant estimates were returned. An in-
ability to find a relationship between the degree of labor heterogeneity and productive
efficiency could be due to the Matching Outcome Effect and Matching Regime effect
cancelling each other out on average, or could be due to the fact that the notion that
dispersion is economically important is non-sense. To make matters worse imperfect
measurement of dispersion and average ability in labor endowments will tend to bias
the estimated impact of dispersion toward zero.

Moreover, the pseudo-Gini coefficient derived from educational attainment levels
does not correspond precisely to likelihood ratio dominance about the mean. Even if
education were measured and mapped into human capital precisely, these measures of
dispersion can only proxy for the sort of variation that impacts matching outcomes as
described above. Fortunately the data do not succumb to the potential for ambiguity
and return statistically and economically significant coeflicients reported in Table 3.3.

The evidence supports the hypothesis that greater levels of dispersion labor en-
dowments reduce aggregate productivity on average. Consistent with the theory
above we can infer that labor exhibit strong preferences for particular job types. Ini-
tially there seem be more detrimental effects on efficiency from dispersion; 61 > 0 .

Eventually losses in productivity begin to reverse (62 < 0) , plausibly due to shifts in

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matching regimes as potential losses in match quality become more severe. Coun-
tries with high levels of dispersion, specifically those with measures greater than 20.8
under constant returns, no longer suffer productivity losses from polarized labor en-
dowments. As expected higher average levels of ability are associated with greater
productivity.

The distribution of educational attainment in labor endowments appears to be
a statistically significant determinant of productivity. Evaluating the economic
significance of the parameters, even interpreting them clearly, is more difficult. Under
constant returns to education the average measure of dispersion across countries is
19.5. Based on the estimates in Table 3.3, a 1% increase in measured dispersion
leads to a 0.7% increase in unit factor requirement for the average country. This
sort of estimate seems plausibly and economically significant. However the meaning
of a 1% change in the measured level of dispersion is an ambiguous description of
how the shape of labor endowments vary across countries. The ideal way to evaluate
the importance of the shape of labor endowments would be to include both country
fixed effects and the measures of dispersion and mean human capital accumulation.
If the fixed effects estimates were estimated at zero, we could infer that productivity
difierences were explained entirely by the shape of factor endowments. Unfortunately
there are not enough degrees of freedom to perform such a test.

A feasible alternative is to consider what would happen to factor requirement
across countries if their labor endowments resembled the shape of the US labor endow-
ment; recall that the Hick-neutral productivity differences in Table 3.2 are estimated
relative to the United States. Korea, Australia and Poland are among the least effi—
cient countries, with unit factor requirements approximately 6.5, 2 and 3 times that
of the US respectively. If they were able to reduce the amount of dispersion (Korea:
21.2, Australia: 17.9 and Poland: 15.7) to the same level of the United States (12.5)

then they could reduce their unit factor requirements in all industries significantly.

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Based on the estimates in Table 3.3 they could almost surpass the United States,
using about 15% less of each factor than required in by US industries. Estimates
of the technological improvements that could be realized if the level of dispersion
in labor endowments for each country were the aligned with the US are reported in
Table 3.4. The estimates gravitate toward .85, suggesting that most countries could
surpass the US in terms of productivity. However this is likely do to the fact that
the US is an outlier in terms of dispersion. The OLS estimates of the partial effects
of variation in levels of dispersion are likely to be imprecise when using the US as a
basis of comparison.

Of course the most relevant way to evaluate the economic significance is to test if
the information about dispersion and average levels of human capital explain inter-
national trade flows. This is the real focus of the paper and will be discussed in the
next section. At this point it is worthwhile to discuss limitations of the estimation
methodology used above. First, the shape of a distribution is described by more than
a mean and level of dispersion (even if perfectly measured). Estimates of factor re-
quirements and the coefficients for measured dispersion likely suffer omitted variable
bias because features of labor endowments such as skewness are not included. Suit-
able measures for higher moments are difficult to construct in addition to dispersion

because only four levels of educational attainment are available for each country.

16.2 Factor Content of Trade

In this section I test the validity of the Vanek prediction that countries will be net
exporters (importers) of their abundant (scarce) factors, controlling for the effect of
dispersion on unit factor demands. With international productivity differences the
amount of each factor embodied in each unit sent abroad varies by exporter. Factor
requirements are given by each country’s technology matrix AC. Let X Cl be the vector

of exports from country c to county j. The factor content of exports, F CW, from

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country c to the world, W, is then
Fcl/V = AcXcIV

The amount of each factor imported by country c from country j is F j C = Aj X j C.
Summing across exporters gives the total imports of both factors for country c. The

net amount of factor trade for country c is given by

FCW — 2 Pic (41)

jaéc
Relative factor abundance is defined in the usual way. Country c is considered
abundant in a particular factor if its endowment, VC, relative to the world endowment,

f, exceeds its share of world GDP, 36. So relative factor endowments are given by
Vfc — sCVfC (42)
The strict statement of the Heckscher—Ohlin—Vanek theorem is

v; — 30fo = FCW — Z We (43)
3756

If actual data on technologies are used and imports are proportional to GDP, then
the Vanek prediction holds as an identity. I avoid this issue first because technologies
are estimated rather than taken as observed. A second reason I am able to circumvent
this problem is that I use bilateral trade data to measure international factor flows,

as opposed to estimating exports based on relative GDP levels.
Tables 3.5, 3.6 and 3.7 provide results from several of the now standard tests
of the HOV prediction in (43). The first, and one of the weakest, is the sign test

based on the various specifications of technology and returns to education. To no

115

surprise, assuming identical technologies causes the HOV theorem to perform poorly;
the measured and predicted factor content of trade have the same sign only 26% of
the time. Also in-line with previous findings, estimated Hicks-neutral technology
differences across countries influence factor trade patterns. Accounting for such
differences, factor endowments correctly predict that a country is a net exporter
(importer) of its abundant (scarce) factor 43% of the time. The key question is
whether or not the shape of labor endowments helps to predict the factor content
of trade. Evidence from the sign test suggests that controlling for the mean, and
level of dispersion, in labor endowments improves factor content predictions just as
well as estimated productivity differences across countries; under constant returns
to education the relative abundance of each factor predicts the sign on the measure
factor content of trade correctly for 43% of country-factor pairs.

The primary weakness of the sign test is that it does not relate the magnitudes
of relative factor endowments and measured factor trade. Larger degrees of rel-
ative factor abundance should be associated with larger amount of exports. The
Spearman Rank tests evaluates this slightly stronger version of the HOV prediction.
Factor endowments39 across countries are ordered in terms of relative abundance.
That ranking is compared to the ordering of factor trade volumes. Here estimated
differences in the shape of endowments perform poorly compared to unexplained tech—
nology differences. In fact the amount of factor trade predicted by relative factor
supplies and the shape of the labor distribution appear at best uncorrelated, and at
worst negatively correlated, with observed factor flows.

The precise statement of the HOV theorem is an identity which can be tested by
regressing the right-hand side of (43) on the left-hand side, as in Davis and Wein-
stein. The theory predicts a coefficient of one. Also the R2 is an indicator of the
amount of missing trade a la Trefler (1995). Results from this regression are in Table

3.7. Again we see that assuming identical technologies does poorly. Both estimated

116

Hicks—neutral technology differences and estimated differences based on the shape of
labor endowments do much better, returning positive and significant relationships be-
tween predicted and measured factor trade. Neither returns an estimated coefficient
statistically close to 1.

Using measures of dispersion and average ability help to explain the pattern of
world factor trade pattern magnitude of factor trade. Estimated HN TD can better
account for trade volumes. To see this note that the missing trade statistic (the R2
from regression tests) is much greater under a the specification of HNTD.

As a robustness check I estimated technology differences that may be implied by
differences in capital-labor ratios across countries which may cause them to operate in
different cones of diversification. See Schott (2003). Using data on the relative sizes
of factor endowments within a country in tandem with the shape of labor distributions
improves the predictive power of the HOV theorem. The sign test is satisfied nearly
50% of the time and the rank test returns a positive and stronger correlation between
predicted and measured factor trade volumes. However is it difficult to discuss the
role of relative factor endowments in the current context. It is not clear from this
analysis how labor would match and sort across different goods within industries;
therefore it would be misleading to suggest that laborers in different countries appear
to match in different diversification cones because capital-labor rations are relevant

statistically. I leave such issues to future research.

17 Conclusion

The primary goal of this analysis has been to demonstrate that factor endowments
still have an important role in the story of international trade. For some time factor
supplies have taken a back seat to unexplained Ricardian productivity differences in

the HOV literature. In world of heterogeneity and team production endowments

117

must be considered as more than cumulative collections of factors. A richer char-
acterization views endowments as distributions with shapes that reflect dispersion,
mean, modal values, skewness and other moments. Moreover, the individual features
of factor distributions interact to shape the pattern of world trade, rather than only
influencing production independently.

Here I found that using information about both the mean and dispersion in labor
endowments improves the ability of relative factor abundance to predict the direction
of factor trade. Countries export their abundant factors as long as they can organize
labor effectively. Benefits attached to particular job types makes the organization
problem more difficult, and dispersion in labor endowments makes poor organization
more costly. For most countries good job types are too enticing. Only in those
countries with a very large degree of dispersion does individual matching behavior
reflect the most productive allocation.

On the other hand the estimated impact of dispersion in labor endowments on
productivity fails to accurately described factor trade volumes suggested by relative
factor supplies. This could be due in part to the fact that some countries can organize
labor for producing exports more or less effectively than production intended for
domestic consumption. This result could also be due to statistical artifacts. As I
have only incorporated two features of the shape of endowments, omitted features
such as skewness may have biased estimates used to construct technology matrices
across countries. There is also likely to be attenuation bias as the distribution of
human capital is certainly measured with a degree of error. Yet, even through a
biased lens, endowments seem to be an important component of international trade

again.

118

Chapter 3-Data Appendix

17.1 Sources

The source of production, factor usages, value added and bilateral trade data is the
2005 volume, ed. 5, of the Organization for Economic Cooperation and Development
STAN database. Observations are available at the industry level described in table A-
1 and taken from the year 1995. Empirical tests of productivity differences make use
of the information in 25 industries covering both manufacturing and service sectors.
However, bilateral trade data for service sectors is incomplete; only an aggregate for
all service industries is reported. The pattern of estimated productivity differences
using only 15 manufacturing industries (those without an asterisk in table A-1) and
the one service industry aggregate (sum of all industries with asterisk in table A-1)
did not differ across countries from the estimates when all 25 industries were used.
For both trade and production data the industry classifications are consistent with
ISIC Rev. 3.

The data source for employment is the Number Engaged (EMPN) for each indus-
try, which includes domestic production. Some variation in reporting employment
data exists across countries. Most countries report a headcount of persons employed.
However Austria, Canada, New Zealand, and Great Britain report the number of
jobs in each industry. The national accounts of employment vary across countries,
as hundreds or thousands of persons, and so a simple conversation is used to convert
all employment data of all countries into a common unit of measurement.

Capital data are based on the national accounts of Gross Fixed Capital Formation
(GF CF). Values are given in national currencies at current prices. Production
and Value Added data are also given at current prices in national currencies. All
these variable were converted to US dollars using 1995 exchange rates in the OECD
Factbook 2008.

119

' "'r» area]

'M_ F.—
_-‘:—...g

 

Bilateral Trade data are reported in thousands of US dollars.

import data are available for each country but rarely correspond. For example the
reported value of Australian imports of Wood Products and Cork from Belgium does
not necessarily equal Belgian exports of Wood Products and Cork to Australia. Only
the export data were used to construct bilateral trade flows as the reporting countries
typically provides the free on board value of exports. Imports for a particular country

and industry were then constructed by summing values of exports to that country in

each industry, across all exporters.

Both export and

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table A-1

Industry Code Description

105 Agriculture, Hunting Forestry & Fishing
1516 Food Beverage & Tobacco

1719 Textiles, Leather, & Footwear

2000 Wood Products & Cork

2122 Pulp, Paper, Printing & Publishing 1
2300 Coke Refined Petrol Products & Nuclear Fuel
2400 Chemical & Cleaning Products

2500 Rubber & Plastics

2600 Other Non-Metallic Products

2728 Basic & Fabricated Metals

2900 Machinery & Equipment NEC

3033 Electrical & Optical Equip.

3435 Ti‘ansport Equipment

 

 

120

err.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table A-1 cont.

3637 Manufacturing NEC

4041 Electricity, Gas, & Water Supply

4500* Construction

5052* Wholesale Trade & Repairs

5500* Hotels & Restaurants

6064* Transportation, Storage & Communication

6567* Financial Intermediation

7074* Real Estate & Renting Business

7500* Public Admin, Defense & Compulsory Social Services

8000* Education

8500* Health & Social Work

9093* Other Community, Social & Personal Services
*-Industries for which trade data were not available.

 

 

 

 

 

The data on educational attainment are detailed in Barro and Lee (2000). The
accompanying data set from the Center for International Development reports ed-
ucational attainment levels across countries every 5 years. For the year 1995 the
percentage of the population over the age of 15 in each country, which reaches each of
four levels of education are observed; the levels are No Schooling, Primary Attained,
Secondary Attained, Higher than Secondary education attained. Groups are mutu-
ally exclusive as they reflect the maximum level of education received by each person.
Educational classifications are comparable across countries as they are based on the
International Standard Classification of Education of 1976. For example Primary
Schooling correspond to a particular set of topics or areas studied, rather than years
of schooling. Education levels can be mapped into human capital more uniformly

than if education levels were not universally defined.

121

Fifi€~€Fj

17.2 Missing Data

Despite the wide coverage across and within countries, several data on capital, em-
ployment and production are missing. The following details which data were missing
by country, industry and variable as well as other irregularities.
Australia

PROD-105, 4041, 4500, 5052, 5500, 6064, 6567, 7074, 7500, 8000, 8500, 9093

GFCF— 1516, 1719, 2000, 2122, 2300, 2400, 2500, 2600, 2728, 2900, 3033, 3435,
3637
France

GFCF—2300 reported negative value set to zero
Hungary

GFCF— 1516, 1719, 2000, 2122, 2300, 2400, 2500, 2600, 2728, 2900, 3033, 3435,
3637
Ireland

PROD- 105, 2300, 4041, 4500, 5052, 5500, 6064, 6567, 7074, 7500, 8000, 8500,
9093

EMPN-2300
Iceland

PROD-3033, 2900, 7500, 8000, 8500, 2300 reported zero value

GFCF- 1516, 1719, 2000, 2122, 2300, 2400, 2500, 2600, 2728, 2900, 3033, 3435,
3637, 5052, 5500, 6567, 7500, 8000, 8500, 9093

EMPN-1516, 1719, 2000, 2122, 2300, 2400, 2500, 2600, 2728, 2900, 3033, 3435,
3637
Korea

PROD-1516, 1719, 2000, 2122, 2300, 2400, 2500, 2600, 2728, 2900, 3033, 3435,
3637, 5052, 5500

EMPN—2300, 2400, 2500

122

 

Norway

PROD-2300, 2400

EMPN— 2300, 2400
New Zealand

PROD—2300, 2400, 2500, 2900, 3033

EMPN— 1516, 1719, 2000, 2122, 2300, 2400, 2500, 2600, 2728, 2900, 3033, 3435,
3637

GFCF- 2000, 2122, 2300, 2500, 2900, 3033, 3435

17.3 Replacing Missing Data

Missing data were replaced in a two-step process similar to the methodology of Davis
and Weinstein (2001). Using averages from countries for which observations were
available for each industry, missing production data were replaced first, and then
missing factor requirement data were replaced using worldwide averages based on
either observed or imputed production values.

To be specific, let 1% C denote the set of industries for which data are unavailable
in country c, and let 5 denote the set of countries for which production data are
available for all industries i. The average share of total production that takes place

in industry i worldwide is given by

’c‘
§:PROD,
p3,: = . 1 A (A1)

2 C

§:§:PROD,

1 1

 

In countries with missing production for at least one industry, the total value of

production must also be estimated. Using the average production shares for each

123

industry from equation A.1, the total share of production observed in each country is

and so total production in country c is approximated by

Z PROD,-
term
300

 

PRODC =

Finally, missing production data are replaced by multiplying total production by the

average share of production for missing industry m E M C.
A C A C
PRODm = psmPROD

The next step is to replace missing data for factor usages based on world averages.
Let 5 denote countries in which capital usage is available for a particular industry i.
Then missing value of capital usage for industry i in country c was imputed using the
average unit capital requirement of countries for which capital usage was observed in
industry i. The following formula describes precisely how missing factor usages were
imputed. Note that production values may be observed or estimated as described

above.

~

C
2 GFCF,k
GFCFf = Ei—Pnoof (A.2)

~

C
Z PRODz’F
1.21

124

Similarly, missing labor data were replaced by

~

C
23EMrwf
EMPNf = H PRODf (A.3)

 

~

C
2 Prior),k
[:21

17.4 Technology and Endowments

The technology matrix gives unit factor requirement for each industry“. The N x 2
matrix of unit factor requirements for all N industries and 2 factors in country c is
comprised of elements Bicf for i = 1...N and f = L, K. The elements Bz-Cf depend
on the assumed specification of production. e.g. when no technology differences are

allowed then
Bff = exp (A2911)

where Aff are the coefficients from running the regression in
Endowment data are given as the sum of each factor used across all industries
for each location. Because the trade data are observed directly, and not constructed

to conform to data identities such as full employment, no scaling of technologies or

endowments is performed once missing data are replaced and technology calculated.

125

Notes

28In fact, the working paper version of this paper (NBER #w10959) claimed that
these "are not particularly interesting parameters." I hope to show that if fact they
are!

29Given the determination of wages in the non-transferable utility setting described
below, all equilibrium matches will be heterogeneous.

3OSee Acemoglu (2007) for a theoretical treatment of equilibrium technological bias.

31Note that no assumptions are made about the relative magnitudes of losses in
labor and capital efliciency. In the empirical section Hicks-neutral technology dif-
ferences are used as a benchmark for discussing the influence that the shape of labor
endowments has on productivity. Though capital and labor productivity can be influ-
enced independently, such estimates are difficult to cast in term of previous literature.
The goal here is to demonstrate that accounting for heterogeneity in endowments can
do just as well as measured productivity differences at explaining trade flows.

32Davis and Weinstein (2001) demonstrated that the factor content of trade is best
explained with a failure of F PE. Here it is unclear how the failure of FPE would
impact matching behavior across countries. Such analysis is left for further research.
To guage the empirical importance of heterogeneity in factor endowmence for the
pattern of factor trade, I will use the traditional specification of the HOV equation
with FPE as a benchmark.

33i.e. the matching correspondence m(-) is monotonic and increasing

34In general, not all workers with be matched with a partner of identical skill
because the matching equilibrium must also satisfy the equal measure condition.
The measure of workers with skill intensive task assignments must exactly equal the
measure of workers with poor task assignments. Therefore for identical workers a, a
small measure of these laborers may match with workers of infinitessimal differences

in skill. See Legros and Newman (2002) and (2007) for further discussion. Similar

126

adjustments are necessary for all matching regimes as the equal-measure condition
must always be satisfied. As this is only a technical adjustment with little impact on
the overall allocation of matches the reader is again referred to matching literature
for more details.

35Grossman (2004) discusses how imperfect labor contracts can influence the pat-
tern of comparative advantage rather than generate Ricardian productivity differ—
ences.

36Australia, Austria, Belgium, Canada, Germany, Denmark, Spain, Finland, France,
Great Britain, Greece, Hungary, Iceland, Ireland, Italy, Korea, Netherlands, Norway,
New Zealand, Poland, Portugal, Sweden, and the United States

37The data on education across education in Barro and Lee (2000) conform to the
International Standard Classification of Education (ISCED 1976). Primary schooling
in each country cooresponds to the same information learned by students, rather than
years of schooling, or within country definitions of levels. The adjustment so that
levels of education match, rather than years of education, are also why the data
reported in Barro and Lee may differ from national reports.

38Technology differences with respect to each factor cannot be estimated without
restriction using the available data. With only a cross-section of countries and
industries there are not enough degrees of freedom to estimate both country and
factor fixed effects.

39To perform the Rank and Regression tests all observations of VC — sci/w and
F CW — 2 F j C are divided by of so that they are expressed in common units across
factorsjaéc

40To be specific, the labor requirement is how many hundreds of persons engaged
needed to produce a $1 million value of output in each industry and the capital
requirement is the number of dollars worth of capital needed to produce $1 worth of

ouput, at current prices.

127

b-3511

Table 3.1: Mean and Dispersion of Labor Endowments across Countrles

 

 

Constant Returns Decreasing Returns Increasing Returns

Mean Mean Mean

Human Human Human

Cap. Cap. Cap.

Dispersion Accum Dispersion Accum Dispersion Accum

Location (gD) (HCA) (gD) (HCA) (gD) (HCA)
Australia 17.9 304.4 9.5 173.0 32.5 981.2
Austria 16.6 278.7 8.8 165.7 30.3 821.9
Belgium 23.7 269.8 12.2 162.3 44.5 793
Candada 18.5 331.7 10.0 180.6 31.8 1161.7
Germany 15.8 286.5 8.4 167.8 28.2 867.1
Denmark 17.7 277.1 8.9 165.1 34.7 816.9
Spain 21.5 256.3 10.9 158.4 41.9 712.1
Finland 17.2 284.8 8.8 167.5 33.0 859
France 20.1 261.5 10.0 160.2 40.5 736.5
Great Britain 22.4 271.1 11.5 162.8 42.0 796.7
Greece 22.1 255 11.4 158.0 42.0 705.6
Hungary 19.2 257.5 9.7 159.0 37.7 712.5
Ireland 19.4 284.4 10.2 167.1 35.5 864
Iceland 19.5 267.6 9.8 162.1 37.9 768.2
Italy 29.8 249.1 15.9 155.3 52.7 693.7
Korea 21.2 294.9 11.8 169.8 35.8 932.3
Netherlands 21.0 284.4 11.2 167.0 37.8 867.4
Norway 10.9 308 5.7 174.6 20.4 982.2
New Zealand 22.3 308.4 1 1.5 173.9 40.7 1019.8
Poland 15.7 266.2 8.0 161.9 30.1 750.4
Portugal 29.1 233.4 14.8 150.3 56.0 612.6
Sweden 14.7 299.4 7.8 171.8 26.7 940.4
USA 12.5 334.8 6.5 181.9 22.7 1164

 

128

Table 3.2: Estimated Hicks-Neutral Technology Differences (HNTD)

 

 

Country 0 standard error Implied 0
Australia 0.784 0.0558“ 2.19
Austria 0.148 0.0560" 1.16
Belgium -0.081 0.0559 0.92
Canada 0.080 0.0554 1.08
Germany 0.162 0.0543“ 1.18
Denmark 0.124 00565" 1.13
Spain 0.268 0.0552" 1.31
Finland -0.003 0.0566 1.00
France 0.027 0.0546 1.03
Great Britain 0.114 0.0548* 1.12
Greece 0.536 0.0569" 1.71
Hungary 0.941 0.0577" 2.56
Ireland 0.107 0.0580* 1.11
Iceland 0.914 0.0668“ 2.49
Italy 0.178 0.0548M 1.20
Korea 1.866 0.0575" 6.46
Netherlands 0.048 0.0556 1.05
Norway -0.001 0.0581 1.00
New Zealand 0.269 0.0612“ 1.31
Poland 1.084 0.0566” 2.96
Portugal 0.539 0.0574" 1.71
Sweden 0.071 0.0561 1.07
USA 0.000 1.00

 

”-indicates signi ticance at 99% level, ‘-indicates signi ficancc at 95% level

Table 3.3: Impact of Dispersion and Average
ability on Aggregate Productlvity

 

Constant Returns

 

 

 

 

 

8 se t-stat
Dispersion 0.1270152 0.017053 7.45
Dispersion’ -0.003057 0.0004043 -7.56
Mean HCA -0.0026643 0.0006142 434
R2 0.945
Decreasing Returns
6 se t-stat
Dispersion 0.2309423 0.0322655 7.16
Dispersionz -0.0101455 0.0014581 -6.96
Mean HCA -0.007157 0.0019528 -3.66
R2 0.945
Increasing Returns
6 se t-stat
Dispersion 0.0612298 0.0092851 6.59
Dispersionz 00008458 0.000119 -7.1
Mean HCA 0.0005997 0.0001136 -5.28
R2 0.945

 

129

Table 3.4: Productivity Differences imposing identical
dispersion measures across countries (=US)

 

 

 

 

 

 

 

Location Relative Productivity
Australia 0.83
Austria 0.85
Belgium 0.83
Canada 0.82
Germany 0.87
Denmark 0.83
‘ Spain 0.81
Finland 0.84
France 0.81
Great Britain 0.82
Greece 0.81
Hungary 0.82
Ireland 0.81
Iceland 0.81
Italy 1.04
Korea 0.81
Netherlands 0.81
Norway 0.92
New Zealand 0.82
Poland 0.88
Portugal 1.00
Sweden 0.91
USA 1.00
average 0.85
Table 3.6: Rank tests of HOV
Table 3.5: Sign tests of the HOV prediction prediction
Specification %-same sign Specification p
Identical Tech 26 Identical Tech 010
Estimated HNTD 43 Estimated HNTD 0.19
Est. Difference in VL CR 43 Est. Difference in VL CR -0.08
Est. Difference in VL IR 41 Est. Difference in VL IR -0.10
Est. Difference in VL DR 41 Est. Difference in VL DR 005
Diff in VL and K/L
Diff in VL and K/L CR 48 CR 0.20
Table 3.7: RegEsion tests of the HOV prediction
Specification [3 p-val (B=l) R2
Identical Tech -0.65 0.000 0.003
Estimated HNTD 0.63 0.003 0.39
Est. Difference in VL CR 0.45 0.0002 0.2
Est. Difference in VL IR 0.44 0.000 0.19
Est. Difference in VL DR 0.44 0.001 0.19
Diff in VL and K/L CR 0.39 0.000 0.15

 

130

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