size, skill and sorting

© 2004 CEIS, Fondazione Giacomo Brodolini and Blackwell Publishing Ltd, 9600 Garsington Rd., Oxford OX4 2DQ, UK and 350 Main St., Malden, MA 02148, USA.

Size, Skill and Sorting

Dale Belman — David I. Levine

Abstract. The rise in inequality between the 1970s and the 1990s and the per-sistent gap in pay between large and small employers are two of the most robustfindings in the study of labor markets. Mainstream economists focus on differencesin observable and unobservable skills to explain both the overall rising inequalityand the size–wage gap. In this paper we model how increasing returns to skill canaffect the size–wage gap both with constant sorting and with size-biased, skill-biased technological change (e.g. if large firms always had access to computers,but small firms gained access to computers with the rise of affordable personalcomputers).

We analyze the Current Population Surveys from 1979 to 1993 to determinewhether large and small employers are converging in terms of mean wages (theemployer size–wage effect), wage structures by occupation and education, charac-teristics of employees, and wage structures by region. We find mixed evidence ofconvergence and no consistent support for any single version of human capitaltheory.

1. Introduction

One of the enduring regularities of labor economics is that large firms pay more than small firms (Brown and Medoff, 1989).The average pay in large firms (more than 1,000 employees) was 36per cent higher than pay in small firms (fewer than 100 employees)in 1979 (Brown and Medoff, 1989). Larger employers are also more

Dale Belman (author for correspondence), School of Labor and Industrial Relations, Michigan State University, East Lansing, MI 48824, USA. Tel: +1 (517)353-3905 (office); Fax: +1 (517) 355-7656; E-mail: [email protected].

David I. Levine, Haas School of Business, University of California, Berkeley,CA 94720, USA. E-mail: [email protected].

Thanks to the Economic Policy Institute, Upjohn Institute, and Institute ofIndustrial Relations at the University of California, Berkeley for financial support.Comments from Gary Charness, Erica Groshen, Daniel Levine, and K. C.O’Shaughnessy are greatly appreciated.

LABOUR 18 (4) 515–561 (2004) JEL D2, J3, L0

likely to provide benefits and these benefits are typically superior tothose provided by smaller firms (Brown et al., 1990).

An important research agenda in the social sciences has beenunderstanding the differences in employees’ and employers’ char-acteristics that account for this very large pay gap. One explanation,suggested by human capital theory, is that the size–wage gap is the result of large firms’ use of production technologies and workorganizations which rely disproportionately on highly skilledemployees. Large firms pay more for highly skilled employeesbecause, in combination with large firm technologies, such workersare more productive and have higher returns than they would atsmall firms. At its root the size–wage gap is, then, the result of sizeserving as a proxy for the skills of the labor force. Controlling forobservable skills such as education and potential experience reducethe size–wage gap by roughly a third, which is consistent with largefirms hiring highly skilled employees.

The dramatic shift in compensation patterns in the USA betweenthe 1970s and the early 1990s can provide additional tests of thesources of the size–wage gap. Specifically, there has been a verylarge increase in returns to observable skills, such as education, andthe roughly parallel increase in inequality among people with iden-tical observed skills (Katz and Murphy, 1992). Some observers haveposited that the rising inequality for apparently similar employeesis due to rising returns to unobserved skills (e.g. Juhn et al., 1993).Davis and Haltiwanger (1991) build on the rising returns to observ-able skills to analyze the rising returns to size among manufactur-ing establishments they document between 1963 and 1986. That is,they note that the rising returns to establishment size is consistentwith (a) higher skills in larger establishments, which explains theinitial size–wage premium; and (b) rising returns to skills thatexplain the rising size–wage premium.

At the same time, the factors that led to rising returns to skill may directly affect both the distribution of employer sizes and thesorting of skills by size class. For example, the spread of micro-computers during the 1980s and 1990s greatly reduced the fixed cost of using information technology. Such reductions presumablyincreased computer use by smaller employers. If skills are comple-mentary to information technology, then the technological shift thatincreased returns to skills may also have increased the relative useof information technology by small employers.

Below we describe the simplest possible stylized model thatpermits these two possibilities, and use the model to draw out the

516 Dale Belman — David I. Levine

© CEIS, Fondazione Giacomo Brodolini and Blackwell Publishing Ltd 2004.

predictions of each set of assumptions. We then develop a newapproach to decomposing the wage over firm size and time toexamine these predictions in general and for specific types of char-acteristics. Using the Pension and Benefits supplements to the May1979 and April 1993 Current Population Surveys, we find little evi-dence of technological change favorable to skilled workers at largefirms. Rather, we find a narrowing of the differences in the charac-teristics of the labor force of large and small firms, in the returnsto the characteristics of those labor forces and in the wages earnedby employees in large and small firms. Thus, our evidence is con-sistent with the hypothesis that the reduction in the costs of com-puting since 1979 has substantially reduced the historic gaps inskills and wages enjoyed by large firms.

Because some of our results on employer size differ from thosethat Davis and Haltiwanger (1991) found for manufacturing estab-lishments, we rerun our decompositions just for manufacturing andat the establishment level. Most components of our decompositionhave the same sign with comparing establishments instead of firmsor looking only at manufacturing instead of at the entire sample.At the same time, the overall size–wage effect rose when we usesamples similar to those of Davis and Haltiwanger, reconciling theapparently different results.

2. Literature review

Human capital theory explains the higher wages paid by largeemployers by assuming that the production technology or workorganization at those firms relies more heavily on both meas-ured and unmeasured skills (e.g. Idson and Oi, 1999a). The re-lationship of firm size to measured skills is consistent with theobserved tendency of large firms to employ more workers withhigher levels of observable skills such as educational attainmentand age. Many studies have confirmed that these observable skillssuch as age and education are higher at larger employers. In addi-tion, a number of scholars have found that larger firms providemore training (see citations provided by Black et al., 1999). At the same time, even extremely careful controls for employee characteristics rarely explain more than half of the size–wage gap.Brown and Medoff (1989) and more recently Idson and Oi (1999b)review this evidence, and Troske (1999) provides recent carefulanalysis.

Size, Skill and Sorting 517


Analysts nonetheless interpret the size–wage differential as evi-dence that high-wage employers have more highly skilled employ-ees (e.g. Davis and Haltiwanger, 1991). In this view, size serves as aproxy for unmeasured skills. Any differences in wages by firm sizethat remain after controlling for measured skills are attributable todifferences in unmeasured skills.

3. Theory

We are concerned with modeling the interaction between size,skill, technological change, and sorting, and require a model richenough to incorporate each of these factors. The following modelis the simplest model that illustrates the interaction of firm size,employee skill level, and different technologies. Specifically, themodel has two size classes, two skill levels, and three possible tech-nologies. Thus, the model is not intended to be realistic but merelyto illustrate the possible interactions among technology, employersize, skill, and wages. We then use this illustrative model to studythe standard version of skill-biased technological change as well asthe alternative that skill-biased technological changes — such as theintroduction of personal computers — lowered the fixed costs of acomputer and, thus, were favorable to smaller firms.

3.1 Firm size

To model firm size, we permit firms to have either one or twoplants.1 Firms with two plants pay a diseconomy-of-scale cost Ci,where Cmin £ Ci £ Cmax. Firms with high diseconomies of scale havelarger values of Ci. There is an exogenous supply of firms with adistribution of C, and free entry of firms with Ci = Cmax.

3.2 Skill

Employees have either low or high skill, with quantities denotedL and H. There are fixed supplies of L and H workers.

In the base case H workers are twice as productive as L workers.In the scenario with skill-biased technological change, the produc-tivity of skilled labor is further enhanced by a factor of technologi-cal change, N, where N = 1 in the first period and N > 1 in the secondperiod.



3.3 Technology

In the first period, firms can operate without advanced technol-ogy (K = 0) or with a mainframe computer (K = 1). Mainframeshave a fixed cost pM. A single mainframe is useful at either one ortwo plants within a firm. Thus, if a two-plant company has a main-frame, K = 1 at both of its plants.

In the scenario with size-biased/skill-biased technologicalchange, PCs become available in the second period. PCs cost ppc,where pM > ppc > 1/2 pM. While mainframes are useful at both plantsof a two-plant firm, a PC is useful (that is, K = 1) only at plantswith a PC.

3.4 Production function

Computers are complementary to skilled labor. A simple pro-duction function with this feature has output (Q) depend on theamount of skilled and unskilled labor (measured in efficiency units)and on access to computer technology:

[1]

Thus, for a firm with only low-skilled labor, L:

[2]

For firms with only highly skilled labor, H:

[3]

With no complementarity between L and H, we assume firmspick only one type of labor. In many equilibria, some or all firmswill be indifferent between hiring H or L workers.

We normalize output price equal to unity.

3.5 Profit maximization

In the first period (when only mainframes are possible), firms haveeight choices: mainframe user or not (K = 0 or 1), a size of one ortwo plants per firm, and low or high employee skill level (L or H).Some of these eight configurations are never profitable, while others’

Q F H K NH Ka= ( ) = ( ) +( )0 2 1, , .

Q F L K L Ka a= ( ) = +( ) -, , .0 1 1

Q F L H K L NH K Ka a= ( ) = + +( )( ) +( ) -, , .2 1 1 1



profitability depends on the firm’s diseconomy of scale costs (C) andthe market wages wL and wH. The formulas for profitability are:

[4]

[5]

Table 1 summarizes the profitability of each of the eight combina-tions. Recall that in the first period N is unity.

3.6 Equilibrium

The equilibrium choices of firms depend on the relative supplyof L and H, the costs of computers pM, and the distribution of dis-economy-of-scale costs C. To fix ideas, we examine cases where pM

is high enough that firms with only low-skilled labor do not find acomputer profit maximizing, and where there is sufficient highlyskilled labor relative to the supply of low-skilled labor that single-plant firms are indifferent between hiring a single H or a single L.The comparative statics results when technology changes are similarin other cases.

Under these assumptions, three types of firms operate in equi-librium: single-plant firms with no computers and low-skilledworkers, single-plant firms with no computers and highly skilledworkers, and two-plant firms with mainframe computers and highlyskilled workers. The zero-profit condition when low-skill, small,computer-less plants operate is

This formula implies that the equilibrium wage for low-skilledemployees is

Single-plant firms with no computers must be indifferent betweenhighly skilled and low-skilled workers. As highly skilled workerswithout computers are exactly twice as productive as low-skilledworkers, their wages also differ by a factor of 2.

w aa aL* .= +( )1

Profits L L L= ( ) ( ) -[ ] =-( )a w a w wa a1 1 0.

Profits of a two-plant firm

L H M= ( ) - - - -2 2 2F L H K w L w H p K C, , .

Profits of a single-plant firm

L H M= ( ) - - -F L H K w L w H p K, , .





Tab

le 1

.Su

mm

ariz

ing

the

mod

el

KS

ize

Ski

llF

irst

per

iod

profi

ts a

nd c

omm

ents

Sec

ond

peri

od

A0

1L

(a/w

L)a/

(1-a

)-

wL(a

/wL)1/

(1-a

)C

omm

on c

ase

B0

1H

(2a a/

wH)a/

(1-a

)-

wH(2

a a/w

H)1/

(1-a

)

C0

2L

Nev

er c

hose

n,as

pay

ing

fixed

cos

t C

has

no b

enefi

tD

02

HN

ever

cho

sen,

as p

ayin

g fix

ed c

ost

Cha

s no

ben

efit

E1

1L

21-a (2

1-a a/

wL)a/

(1-a

)-

wL(2

1-a a/

wL)1/

(1-a

)-

p MW

e as

sum

e th

at m

ainf

ram

e co

mpu

ters

are

cos

tly

enou

gh

that

it is

not

pro

fitab

le t

o ru

n th

em in

sin

gle-

plan

t fir

ms

F1

1H

(21+

a [21+

a a/w

H]1/

(1-a

) )a-

wH[2

1+a a/

wH]1/

(1-a

)-

p MT

his

case

occ

urs

afte

r P

Cs

are

intr

oduc

edW

e as

sum

e th

at m

ainf

ram

e co

mpu

ters

are

cos

tly

enou

ghth

at it

is n

ot p

rofit

able

to

run

them

in s

ingl

e-pl

ant

firm

sG

12

L2[

[21-

a (a21-

a /wL)1/

(1-a

) ]a-

wL(a

21-a /w

L)1/

(1-a

) ] -p M

-C

We

assu

me

that

mai

nfra

me

com

pute

rs a

re c

ostl

y en

ough

that

it is

not

pro

fitab

le t

o ru

n th

em w

ith

low

-ski

lled

labo

rH

12

H2[

[21+

a [21+

a a/w

H]1/

(1-a

) ]a-

wH[2

1+a a/

wH]1/

(1-a

) ] -p M

-C

Com

pani

es w

ith

very

low

dis

econ

omie

s of

scal

e re

mai

n he

re a

nd k

eep

mai

nfra

mes

Not

es:

The

tex

t di

scus

ses

case

s w

here

sce

nari

os A

,B a

nd H

hol

d in

the

firs

t pe

riod

.Res

ults

are

sim

ilar

wit

h th

e va

lues

of

C,p

Man

d ot

her

para

m-

eter

s su

ch t

hat

othe

r eq

uilib

ria

init

ially

hol

d.In

add

itio

n,if

som

e fir

ms

had

econ

omie

s of

scal

e an

d sc

ope

that

mad

e op

erat

ion

as t

wo-

plan

tfir

ms

effic

ient

eve

n w

itho

ut t

he u

se o

fco

mpu

ter

tech

nolo

gy (

that

is,C

min

wer

e ne

gati

ve),

row

s C

and

D m

ight

not

be

empt

y.T

he r

esul

ts a

rero

bust

to

thes

e ca

ses.

Firms with high diseconomies of scale Ci choose to operate asingle plant without computers, while firms with low Ci choose tobe two-plant firms with a mainframe. The critical value of scale diseconomies is

such that firms with diseconomies of scale Ci > C* operate as single-plant firms, while those with Ci < C* operate as two-plant firms witha mainframe. The critical value C* is higher (more firms choose tobe two-plant firms) when computers are more productive, com-puters are less costly (pM declines), and the relative price of theskilled labor declines (wH/wL falls).

3.7 Skill-biased technological change

We model skill-biased technological change as an increase in N,the productivity of highly skilled labor. With higher N, more firmsoperate two-plant firms, wages for skilled workers rise relative tounskilled workers, average wages of two-plant firms rise relative to those of single-plant firms, and a higher proportion of highlyskilled workers are employed at two-plant firms. Allowing for skill-biased technological change, the profit function in two-plant firmsusing highly skilled labor is

When N = 1, as is the case in the first period, the profit functionsimplifies to the Case H function in Table 1. The change in thecutoff value of C in response to skill-biased technological changeis

C N N a w

w a w

a a a a a a a

a a

*

.

= ( ) ( ) [ ][ ]ÈÎÍ

- [ ] ] >

-( ) + + -( )

+ -( )

2 2 2

2 0

1 1 2 1 1 1

1 1 1

H

H H

2 2 2

2

1 1 2 1 1 1

1 1 1

N N a w

w a w p C

a a a a a a a

a a

-( ) + + -( )

+ -( )

[ ][ ]ÈÎÍ

- [ ] ] - -

H

H H M .

C a w w a w

p a w w a w

a a a aa a

a a a

*

,

= ( )[ ] - [ ] ]{ }- - ( ) - ( )[ ]

+ + -( ) + -( )

-( ) -( )

2 2 2 21 1 1 1 1 1 1

1 1 1

H H H

M L L L

w a wa aH L* *.= =+( )2 21



Some firms whose value of C previously dictated operation as low-skill, single-plant firms without computers now find it profitable tooperate as two-plant firms using computers in combination withhighly skilled labor.

3.7.1 Introduction of the PC. An alternative hypothesis to size-neutral skill-biased technological change is that of size-biased, skill-biased technological change. Thus, assume that N remains constantand instead assume a new technology arises for low-cost comput-ers that operate in only one plant. (We are discussing PCs in the1980s and early 1990s here, not networked computers that mighthave large effects on coordination costs across plants.) We assumethat PCs cost less than mainframes but are useful only at a singleplant. To ensure that some firms retain the two-plant structure, weassume that

Profits for a two-plant firm remain as above in equation [5]. In thissituation, no single-plant firm would ever choose the more expen-sive mainframe, while no two-plant firm would choose PCs. Thus,the new profit function for a single-plant firm is

The maximum profits for a single-plant firm with a PC and low-skilled labor is now

while profits for single-plant firms with PCs and highly skilled laboris

As before, we will examine only a single case, where it is profitableto operate with PCs and highly skilled workers, but not with PCs andlow-skilled workers. Results are similar in the other equilibria.

In equilibrium the marginal firm with a mainframe is indifferentto becoming a highly skilled firm with PCs. Firms adopt main-

Profits H H H pc= [ )( ) - [ ] -+ + -( ) + -( )2 2 21 1 1 1 1 1 1a a a a

a aa w w a w p .

Profits L L L pc= ( ) - ( ) -- - -( ) - -( )2 2 21 1 1 1 1 1a a a a a a

a w w a w p ,

Profits of a single-plant firm

L H pc= ( ) - - -F L H K w L w H p K, , * * * .

12 p p pM pc M< < .



frames only if the mainframe plus the diseconomies of scale costless than two PCs. Thus, the critical value of economies of scale(C¢) is:

Firms with high diseconomies of scale C > C¢ operate as single-plant firms with a PC, while those with C < C¢ operate as two-plantfirms with a mainframe.

In equilibrium, single-plant firms must be equally profitable usingPCs and highly skilled labor or no PCs and low-skilled labor. Low-skilled wages remain equal to their original value. Consistent withthe evidence, the introduction of PCs increases the returns to skills,as highly skilled wages rise after the introduction of PCs:

Proof. Before the introduction of PCs, the profits of single-plantfirms using low-skilled labor without computers were

and these were equal to the profits of single-plant firms using highlyskilled labor without computers which were:

PCs become available in the second period. We assume that highlyskilled plants find computers profitable, that the profits of a single-plant firm using highly skilled labor and a PC are greater than theprofits of a comparable firm that does not use PCs. The profits ofa single-plant firm with a PC and highly skilled labor are

These are again equal to the profits of a single-plant firm using low-skilled labor without computers. This implies that, in the secondperiod, the profits of a single plant with highly skilled labor withouta PC are less than the profits of a PC-less, low-skilled firm:

a w a w w a w a w wa a a a a aL L L H H H( ) ( ) -[ ] > ( ) ( ) -[ ])-( ) -( )1 1 1 1

2 2 .

2 2 21 1 1 1 1+ -( ) + +( ) [ ]( ) -[ ]) -a a a a aa w a w w pH H H pc.

= ( ) ( ) -[ ])-( )2 2

1 1a a a aa w a w wH H H .

a w a w wa aL L L( ) ( ) -[ ]-( )1 1 ,

¢ > ( ) ¢+( )w wa aH L22 1 .

C p p¢ = -2 pc M.



This is only compatible with the first period profit condition if wH

rose relative to wL in the second period.QED

Another hypothesis is that the introduction of PCs raises the efficiency of one-plant firms relative to two-plant firms. As a result,C¢ > C*.

Proof. Consider the marginal two-plant firm with highly skilledlabor and a mainframe, which at the old wH is indifferent betweenoperating in its current incarnation or as a one-plant firm with nocomputer and with low-skilled labor. We have demonstrated that,still holding wH at its old level, the profits of a single-plant firm withhighly skilled workers and a PC are greater than those of a one-plant firm with low-skilled labor and no PC. It must then be thatprofits are also higher than operating at a two-plant, highly skilledfirm with a mainframe. With the option of buying a PC, it will nowcease operating as a two-plant firm and operate as a one-plant firmwith highly skilled labor and a PC. Thus, at the original wages, morefirms operate as one-plant firms. This effect is amplified by the risein wages for highly skilled workers, as these workers are employedintensively by large firms with mainframes.

QED

Given the C¢ > C*, the number of large firms has declined. Coup-ling this effect with higher wH, total employment at large firms alsodeclines. Moreover, more highly skilled workers are now employedat small plants, so the correlation of employer size and skill hasdeclined.

3.7.2 Comparing the two models. Whether the skill-biased techno-logical change was size neutral or biased toward smaller firms, wehave our first hypothesis:

H1: Returns to skills increased.

When the technological change was size neutral we have:

H2A: Highly skilled workers were increasingly concentrated at largefirms.

This is the implicit model of, for example, Davis and Haltiwanger(1991). In addition, size-neutral technological change implies:



H3A: The wage gap between large and small firms increased.

In contrast, when technological change was biased toward single-plant firms we have:

H2B: Highly skilled workers were less concentrated at large firms.

In addition, as large firms with highly skilled workers split to takeadvantage of new small-scale computing technologies we have:

H3B: The wage gap between large and small firms decreased.

In either model, the returns to skills increased and large firms hireddisproportionately skilled workers. Thus, both models predict:

H4: Returns to characteristics common at large firms have risen:

The specific models we examined made a number of strong assump-tions and examined only a subset of possible initial configurations.These basic results are robust to wide variations in the initial con-ditions, provided the introduction of personal computers inducessome previously two-plant firms to switch to single-plant operationand provided computers remain complementary to skills.

Most importantly, we are using the model to classify one-plantfirms as ‘small’ and two-plant firms as ‘large’. In fact, the model hasendogenous employment per plant as well as endogenous plants perfirm. The results are unchanged when we account for this additionalfactor.

Moreover, our model of technological change and rising com-puter use in small firms (measured as fewer plants per firm) canalso be used to study firm size measured as employees per estab-lishment. To see this result, assume there are several vertically integrated departments in large plants. An advantage of the largeplants initially is that they permit economical use of a large mainframe, and this advantage outweighs any diseconomies thatmay arise. Such diseconomies of scale may arise, for example, fromlower powered incentives within organizations compared to markettransactions. Now when PCs become affordable, two smaller plants (each with a PC) may be more profitable than a single largeplant with a mainframe. That is, by reinterpreting ‘plant’ as ‘depart-ment’ our results generalize directly from operating one large vertically integrated plant versus operating two smaller plants.Thus, our hypotheses about reductions in firm size also apply toestablishments.



In a richer model, PCs might increase the efficient scale of smallenterprises. Thus, as usual, theoretical models are consistent with awide array of evidence. We will revisit this issue when we turn tothe data.

4. Methods: decomposing changes in the size–wage gap

Several of our hypotheses address the size–wage gap: hypothesis3A suggests that skill-biased technological change will widen thegap; 3B suggests that size-biased technological change will narrowthe gap. Changes in the size–wage gap have typically been measuredas the change in relative returns to firm size or as the change inreturns controlling for individual characteristics, occupation andindustry structure. Using such approaches, Boden (1997), Belmanand Groshen (1998), and our analysis (Table 3) have found, consis-tent with the second hypothesis, a narrowing in the overall gap.

Changes in the size–wage gap are not, however, simply a matterof overall returns to size. Changes in the gap may reflect changesin the characteristics and the rewards to characteristics of the laborforces of large and small firms. Several of our hypotheses addressunderlying sources of changes in the gap rather than movement inthe gap itself. Just as a Oaxaca decomposition provides consider-ably more information than indicator variable models about differ-ences in the structure of wages between different racial, gender orsectoral groupings, we can learn considerably more about how thesize–wage has changed over this period through a decompositionof the structure of wages over time and firm size. As this decom-position is more complex than the typical Oaxaca, we lay out bothour approach and the interpretation of the components of thedecomposition before presenting our results.

We model the log wage as a function of demographic and humancapital factors, occupation, and location, as well as employer size.We estimate separate log wage equations in each year (1979 and1993) for large and for small firms:

and

W X b eti ti t tiS S S S= ◊ + .

W X b eti ti t tiL L L L= ◊ +



In these equations, Wti is the log(wage) for person i, Xti is the vectorof characteristics for person i, while bt is the vector of coefficients.The superscripts L and S refer to large and small employers, andthe subscript t refers to the year 1979 or 1992.

Subtraction across years and size classes yields the change in theaverage size–wage gap: (W L

93 - W S93) - (W L

79 - W S79). For notational

simplicity, define the change in the large versus the small gap inmean characteristics as

and define the change in the large–small gap in coefficients as

After tedious algebra, the change in the size–wage gap can berewritten as the sum of four meaningful components:

(A) [6]

(B) [7]

(C) [8]

(D) [9]

We discuss each component of this decomposition in turn. For thefirst term in each component (those without a year subscript), weaverage 1979 and 1993 values. We discuss the cases where choice ofweights affects the results.

4.1 (A) Have returns at large and small firms converged?

The term X S ·D(B gap) measures the changing difference in coefficients between large and small employers. X S, the mean characteristics of small firm employees (averaging 1979 and 1993characteristics), weights the change in the coefficients gap,aggregating the changes of the individual coefficients into a singlemeasure. If this term is negative, large- and small-firm coefficientshave converged.

X X b b93 79L L L S-( ) ◊ -( ).

X X b bL S L L-( ) ◊ -( ) +93 79

b XS ◊ ( ) +D gap

X BS ◊ ( ) +D gap

W W W W93 93 79 79L S L S-( ) - -( ) =

D B b b b bgap L S L S( ) = -( ) - -( )93 93 79 79 .

D X X X X X X X X Xgap L L S S L S L S( ) = -( ) - -( ) = -( ) - -( )93 79 93 79 93 93 79 79



4.2 (B) Are employee characteristics at large and small firms converging?

The term bS ·D(X gap) measures the changing gap in character-istics between large and small employers. Here, the small-firm coefficients, bS (averaging 1979 and 1993 coefficients), are weightsthat aggregate the change in the characteristics gap into a singlemeasure. If this measure is negative, then large- and small-firmcharacteristics have converged (as in hypothesis 2B, not 2A).

4.3 (C) Are returns rising for characteristics common at large firms?

The term (X L - X S) · (bL93 - bL

79) measures the effect of changingcoefficients on the characteristics particularly common at largefirms. The first component of this term, the ‘weights’ used to aggre-gate the coefficients, is the difference between the characteristics of large and small firms. The second element is the change in thereturns to large firms’ characteristics between 1979 and 1993. If theterm is overall negative, returns to characteristics particularlycommon to large firms have declined.

The point may be illustrated using a single characteristic, educa-tion, as an example. Large firms had higher average education thansmall firms in both 1979 and 1993, so the first element is positive.Given that returns to education rose throughout the economy, thesecond element is also positive. The education component wouldthen serve to increase this term, and widen the gap between large-and small-firm wages.

If large firms sorted on higher skills and returns to skills rose inthe economy, then human capital theory suggests: hypothesis 4,returns to characteristics common at large firms have risen. Thishypothesis suggests that this term is positive:

4.4 (D) Do employees at large firms increasingly have thecharacteristics that large firms reward well?

The term (X L93 - X L

79) · (bL - bS) measures whether the character-istics at large firms have become more concentrated in areas wherelarge firms pay above-average returns. The first component is thechange in the mean characteristics of large firms between 1979 and

X X b bL S L L-( ) ◊ -( ) >93 79 0.



1993. The second, the weighting component, measures the excessreturns provided by large firms, relative to small firms, in year t. Ifthis term is negative, then large firms have hired fewer employeeswith characteristics that they compensate particularly well. Forexample, large firms on average pay higher returns to educationthan do small firms. If the average education levels at large employ-ers have risen, this term will increase.

5. Data

We analyze the pension and benefits supplements to the May1979 and April 1993 Current Population Surveys (CPS). A require-ment for this analysis is the employment size of each respondent’semployer. The benefits supplements are the largest micro-datasample of the US labor force with such information.2 In addition,the benefits supplements collect data on wages, pensions, healthbenefits, and tenure with the current employer, which is useful tothis investigation. We analyze the work force ages 16–75 excludingthe self-employed, those employed in business services, thosereporting wages of under $1.00 per hour or more than $100.00 perhour and those with missing data. The public sector is excludedfrom our analysis because their labor markets and career systemsoperate differently from the private sector. Agriculture is omitteddue to concerns about in-kind income. We also omit business serviceindustries. The 1979 wage data have been converted into real dollarsusing the CPI-U-X1.

There is no universally accepted definition of large and smallemployer; indeed, there is disagreement over whether size should bemeasured by employment or by capital stock (Belman and Groshen,1998). We treat employers with 1,000 or more employees as largeand those with fewer than 100 employees as small. In most of ouranalyses we omit medium-sized employers (100–999); their resultsare discussed in the robustness checks.

Our typical regression specification incorporates controls for age,its square and education, and indicator variables for marital status,union membership, race, gender, residence in a metropolitan area,and major occupation. The education variable reported in the CPSwas changed from a measure of years of education completed to a measure of degree attainment in 1992. We have converted themeasure of degree attainment back into a measure of continuouseducation using an algorithm provided by Jared Bernstein.



5.1 Methodological issues

We present both descriptive statistics and regression to analyzechanges in large and small firms between 1979 and 1993. Sampleweights are needed to obtain representative descriptive statisticsfrom the CPS. So that decompositions add up correctly, regressionsare also weighted. Because we include the factors that are used instratifying the CPS (race, age, etc.) in our regressions, the weightedand unweighted regressions are essentially identical. The standarderrors of the regression estimates are obtained using the Huber–White correction for heteroskedasticity.

6. Results

We first examine the distribution of employment at large andsmall firms, and then we examine the size–wage effect. Finally, welook at the relation between wages at large and small employers ina region.

6.1 Background: has the typical employee’s employer size declined?

The proportion of employment at very large employers rosebetween 1979 and 1993 (see Table 2).3 Large employers (over 1,000employees) employed 41 per cent of the sample in 1979, rising to45 per cent in 1993. This increase was matched by declining em-ployment in small (under 100) employers from 40 to 34 per cent ofthe sample. The employment share of middle-sized firms remainedstable through this period.4

One source of this shift toward larger firms might be a shift inemployment toward industries with larger firms. This effect is exam-ined in the last column of Table 2, which weights the 1993 firm size



Table 2. Distribution of employment by firm size

1993 (%)Firm size 1979 (%) 1993 (%) (1979 industry weights)

Under 100 39.6 34.2 34.9100–999 19.7 20.9 20.81,000 plus 40.8 45 44.1

employment distributions for major SIC industries by their 1979employment. The results are similar to the estimates in column 2;the shift toward larger firm size is not the result of changing pat-terns of employment by industry. (A rising share of employment at large employers provides only weak evidence in the debate onwhether small employers create a disproportionate number of jobsbecause the population of employers in the ‘large’ category changesover time; see Davis et al., 1996.)

These results are broadly consistent with the hypothesis that skillswere more valuable in the later period, and, thus, that skills-intensive large firms grew as a proportion of the economy.

The stable share of employment holds up in most of the 12 majorindustries included in this study (see Table A1). The large-employershare declined in mining, durable goods, communications and util-ities, and rose in retail trade and in non-business service industries.The results on regression-adjusted wages are also similar if we lookat employment by establishment size instead of employer size (seeTable A2).

6.2 Has the size–wage effect declined?

We first present the mean wages paid by large and small firms in1979 and 1993, and then the difference conditional on employeecharacteristics (age and its square, education, and indicator vari-ables for marital status, union membership, race, gender, residencein a metropolitan area, and 11 major occupations). The real wageat middle-sized and large firms declined between 1979 and 1993,while small firms’ wages remained constant (see Table 3). While realwages of small firms remained around $10.20 per hour (in 1993dollars), the wage at middle-sized firms fell by 50 cents per hour,from $12.57 to $12.05, and the wage at large firms declined from$14.61 to $13.34. This corresponds to a decline in the large firmwage advantage of 9.6 log points between 1979 and 1993, or almosta third of the total pay advantage at large employers.

Regression estimates of the size–wage effects parallel the changein unadjusted means, but are less marked. The wage advantage ofmiddle-sized firms relative to those with fewer than 100 employeesfell from 11.3 per cent to 7.8 per cent, from 10.7 to 7.5 log points,between 1979 and 1993. The percentage point drop for employeesin the largest firms, from 20.3 per cent to 15.3 per cent, was somewhat larger than that of the workers in middle-sized firms.Although not the emphasis of this paper, a similar decline in the



size–wage effect shows up between large and small establishmentsas between large and small employers (see Table A3).

6.2.1 Decomposing sources of wage changes. The decompositionfrom equation [1] permits us to understand whether the changingwage patterns at large and small employers are due to sorting or tochanges in sector-specific returns to characteristics. Estimates ofregression coefficients by firm size and year are shown in Table A4,and mean characteristics by firm size are shown in Table A5.The specification of the model follows that used in prior modelsreported in this paper except that the age, education, and tenurevariables have been re-centered on their means and a quadratic termhas been added for age (age2).

Table 4 summarizes the decomposition. The returns to large firmsdeclined by between 9.6 and 13.2 percentage points between 1979and 1993, depending on whether 1979 or 1993 weights are used. Thedecline was caused by convergence in returns at large and smallfirms (the gap between BL and BS declined between 1979 and 1993)(part (A)) and by a decline in the gap in characteristics of large andsmall firms (part (B)). Using 1979 characteristics and coefficients asthe baseline, the convergence in returns accounted for 78 per centand the convergence in characteristics accounted for 130 per centof the 9.6 percentage point decline in the large-firm wage. With a1993 base, the decline was 64 per cent and 92 per cent, respectively.



Table 3. Firm size effects on wages, 1979–93

1979 1993

Real wage by firm size (1993 dollars)Under 100 employees $10.19 $10.24100–999 employees $12.57 $12.05Gap in log wage over small firm wage 0.210 0.1631,000 or more employees $14.61 $13.34Gap in log wage over small firm wage 0.360 0.264

Regression estimates of medium- and large-firm effects on log(wage) (t-statistics in parentheses)

100–999 0.107 0.075(11.1) (7.9)

1,000 plus 0.185 0.142(23.1) (18.1)

Notes: Control variables are listed in Table A2. Small employers (<100) are the omitted category. Deflation uses the CPI-U-X1.



Tab

le 4

.D

ecom

posi

ng c

hang

es in

the

siz

e–w

age

gap

Com

pone

nts

ofth

e19

79 b

ase

1993

bas

e

size

–wag

eD

escr

ipti

on o

fsi

ze–w

age

Siz

e–w

age

Siz

e–w

age

deco

mpo

siti

onco

mpo

nent

gap

% o

fga

pga

p%

of

gap

Ove

rall

chan

ge in

siz

e–w

age

-9.6

pp-1

3.3p

pga

pA

XS·D

(Bga

p)H

ave

retu

rns

at s

mal

l and

-7.5

pp78

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.4pp

63.2

larg

e fir

ms

conv

erge

d?B

bS·D

(Xga

p)A

re e

mpl

oyee

cha

ract

eris

tics

-12.

5pp

130.

2-1

2.2p

p91

.7at

larg

e an

d sm

all fi

rms

conv

ergi

ng?

C(X

L-

XS )·

(bL 93

-b

L 79)

Are

ret

urns

ris

ing

for

8.2p

p-8

5.4

7.2p

p-5

4.1

char

acte

rist

ics

part

icul

arly

com

mon

at

larg

e fir

ms?

D(X

L 93-

XL 79

)·(b

L-

bS )D

o em

ploy

ees

at la

rge

firm

s 2.

22pp

-23.

10.

1pp

-0.8

incr

easi

ngly

hav

e th

ech

arac

teri

stic

s th

at la

rge

firm

s re

war

d w

ell?

Not

es:

pp =

perc

enta

ge p

oint

.T

he s

ize–

wag

e ga

p is

the

wag

e ga

p be

twee

n la

rge

firm

s (m

ore

than

1,0

00 e

mpl

oyee

s) a

nd s

mal

l fir

ms

(few

er t

han

100)

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ium

-siz

ed e

mpl

oyer

s ar

e om

itte

d fr

om t

his

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ysis

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n ch

arac

teri

stic

s an

d co

effic

ient

s by

siz

e cl

ass

and

year

are

pre

sent

ed in

Tab

le A

4.

These trends were partially counterbalanced by improvements inthe returns to characteristics common at large firms over time (part(C)) and improvements in the characteristics of employees of largefirms between 1979 and 1993 (part (D)). The former increased thegap between large- and small-firm wages by between 85 per cent(1979 base) and 54 per cent (1993 base), the latter by between 23per cent and 0.8 per cent. We now analyze each component of thedecomposition in more detail.

6.3 (A) Are large and small employers paying more similar returns?

Overall, the decomposition indicates that the returns have con-verged between large and small employers. Using the 1979 base, theconverging coefficients knocked out 7.5 percentage points of thesize–wage effect — almost half of the 18.5 per cent advantage esti-mated in Table 3.

Appendix Table A4a indicates which coefficients converged.Focusing on the 1979 base (the first three columns), the first columncontains the small-firm variable means for 1979, the second columnis the change in the large/small gap in coefficients between 1979 and1993, and the third column is the product of the first two columns.For example, the returns to education rose at both large and smallfirms from 1979 to 1993, but rose fastest in small firms. Thus, thegap in returns to a year of education in large and small firmsdeclined by 1.44 percentage points between 1979 and 1993. Theeffect of this convergence in returns to education was to reduce theoverall size–wage gap by 0.16 percentage points.

No single relative return of large versus small firms changed substantially. The largest single change between 1979 and 1993 isthe decline in the gap between the intercepts of 20.1 percentagepoints (see Table A4). After allowing for the effect of the intercept,the balance of the shift in the gap is a positive 12.6 per cent (or 11.7per cent for the 1993 weights). Given how we measured the vari-ables, the intercept indicates the effect of changing returns to sizefor male employees with mean education, age and tenure living inthe West, working as laborers and employed in the retail trade.

The allocation of the effect of the change in the coefficient gapbetween the intercept and other coefficients varies depending on thechosen omitted category for occupation, region, sex, and industry.Almost any change in the omitted category reduces the size of thechange in the gap of the large- and small-firm intercepts over time.



Nevertheless, under almost any characteristics (other than omittingthe small occupational group ‘Technicians’), the intercepts haveconverged. These changes suggest that large firms are paying lesssimply because they are large (the convergence of the intercepts),while increasing their payments for most employee characteristics.5

Turning to specific coefficients, the most notable decline in thecoefficient gap is a 1.4 percentage point decline in the large-firmeducation advantage (see Table A4). In contrast, large firms’ excessreturns rose for being female; living in the Northeast, Midwest andSouth; being employed as a precision production operative (craftworker) and working in non-durables manufacturing (see TableA4). The change in relative returns is not significant for most indi-vidual coefficients; at the same time, many more shifts are positivethan negative. These positive shifts substantially outweigh the negative, creating an overall effect of a rising gap between large and small firms (see Table A4). Only the declining difference inintercepts leads to converging coefficients.

6.4 (B) Are employees’ characteristics at large and small firms converging?

Table A5 presents tabulations of mean education, tenure, poten-tial experience (age — years of schooling — 6), race, gender andunion status by employer size in 1979 and 1993, as well as thechange in the gap in large and small means between 1979 and 1993.In 1979, employees of large firms were older (mean age 36.5 yearsat large employers against 35.4 years at small employers) and moreeducated (12.7 years of education as opposed to 11.9). Employeesat large firms were far more likely to be in a union (33.9 per cent asopposed to 9.5 per cent) and had almost twice the tenure (8.9 yearscompared to 4.5).

We measure the total effect of changing relative characteristicsby weighting characteristics by the coefficients of the wage equa-tions used in the size–wage decomposition. If the weighted sum D(X gap) ·bS(see equation [7]) is negative, then characteristics are,on average, converging. On average, the characteristics of em-ployees at large and small firms converged between 1979 and 1993.This convergence would have over-predicted the decline in the size–wage effect, reducing it by 12.2 log wage points. This calculation ispresented variable by variable in Table A5.

Most notably, the percentage of workers organized at large firmsdeclined from 33.9 per cent to 19.2 per cent. This decline of 14.7



percentage points was considerably larger than the correspondingdecline from 9.5 to 4.8 per cent at small firms. The more rapidabsolute decline of unions at large firms lowered the size–wage gapby about 2.4 percentage points (see Table A4b). Before making toomuch of the change, it is important to note that while the absolutegap declined, at the same time the ratio of union membership atlarge versus small firms actually increased.

The characteristics that relate most closely to human capitaltheory are age, tenure and education. None exhibited the increasesin sorting coupled with rising returns to skill predicted by humancapital theory (hypothesis 2A); instead, sorting declined slightly(consistent with hypothesis 2B). The gap in age between large andsmall firms fell from 1.2 years to 0.5 years between 1979 and 1993.The difference in education fell more modestly, from 0.8 to 0.7 years.Mean tenure was almost constant at large employers, declining from8.8 to 8.5 years — well within the sampling error — but rose from4.5 to 4.9 years at small employers. Relatively small change in levelsand patterns of tenure during this time period has been found in theCPS by other researchers such as Diebold et al. (1997).

Overall, convergence in factors acted to reduce the gap in wagesbetween large and small firms. The change in age reduced the gapby 0.3–0.4 percentage points, which in tenure reduced the gap by0.7–0.9 percentage points. The declining gap in education betweenlarge and small firms reduced the wage gap by between 0.3 and 0.5percentage points.

Shifts in occupation and sectoral distribution of employmentalso influenced the size–wage gap. Although there were only modestchanges in the occupational and industry distribution of employ-ment in small firms, the industry distributions at large firms shiftedsubstantially. Most importantly, the proportion of employees inlarge firms employed in the durable goods industries declined from 32.4 per cent in 1979 to 18.2 per cent in 1993 (see Table A5).Durable goods are a high-wage sector for both large- and small-firmemployees. Thus, the decline in employment in durable goods inlarge firms reduced the large-firm wage advantage by between 2.8and 3.8 percentage points (see Table A4b).

Small firms remained about 50 per cent female through the1979–1993 period, but large firms increased from 35 to 46 per centfemale. Given the lower wages of women, this convergence loweredthe size–wage effect by about 2 percentage points (see Table A4b).

In contrast with most characteristics, employment of blackworkers diverged. Even in 1979, employees at large companies were



more likely to be black than their counterparts in small companies(8.7 per cent black versus 7.6 per cent). This relatively high employ-ment of blacks at large employers increased somewhat in recentyears from 0.9 per cent higher to 2.3 per cent higher than the small-est sized firms.

Thus, these results are consistent with declining barriers to femaleand minority employment at large firms (consistent with H4),although the 1979 results did not show the lower percentage ofblack workers at large employers that theories of segmented labormarkets predicted. (Holzer, 1998, further discusses the evidence andtests several explanations for the lower representation of blacks insmaller establishments.) Because the wages of black workers arelower than those of other racial groups, the increasing proportionof blacks at large firms causes a 0.4 percentage point decline in thesize–wage gap.

In short, with the exception of race, the mean characteristics ofemployees at large and small employers have either remained con-stant or have converged substantially between 1979 and 1993. Theseresults run counter to the hypothesis that sorting of worker skillsby employer size has increased.

6.5 (C) Are returns rising for characteristics common at large firms?

If large employers specialize in highly skilled workers (relative tosmall firms) and returns to skills have risen (relative to returns in1979), we should see rising returns to characteristics that arecommon at large firms. Formally, this theory implies that term (C)from the size–wage decomposition, (bL

93 - bL79) · (X t

L - X tS), is posi-

tive. For example, the combination of rising returns to education(regardless of employer size) coupled with higher average educationat large firms increases the gap between large- and small-firm wages.

Overall, rising returns for characteristics common at large firmshave widened the wage gap by between 7.2 (1993 weights) and 8.2 (1979 weights) percentage points (see Table A4c). This resultsupports the hypothesis that large firms specialize in highly skilledworkers and that returns to these skills have increased.

Most specific characteristics with rising returns showed the samepattern. Returns to education at large firms rose by 1.4 per cent andwidened the gap by 1.1 percentage points, and returns to job tenureincreased by 0.6 per cent and widened the gap by 2.7 percentagepoints. Returns also rose substantially for being a union member



and being employed in the production of non-durable goods (wherelarge firms are over-represented); returns fell substantially for con-struction employees (where large firms are under-represented).

6.6 (D) Do employees at large firms increasingly have thecharacteristics that large firms reward well?

Finally, large employers might have become more or less inten-sive employers of employees whose characteristics they compensateparticularly well. In fact, this effect is small, accounting for betweena +0.1 and +2.2 percentage point increase in the size–wage gap. Thiseffect is driven by declining unionization of large-firm employees,coupled with the higher returns to unionization at large employers.No other factor is associated with as much as a 1 percentage pointchange in the size–wage gap.

7. There is more to the story

At this point we have a simple story: the employer size–wage gap declined as characteristics converged, even as returns rose forcharacteristics common at large firms. An optimistic reader mightnote that these results follow those predicted by our model ofsize-biased, skill-biased technical change (where microcomputersare now cost effective at small enterprises) and expect the paper toend here.

In fact, the story is more complex than that simple pattern. Inthis section we elaborate these results along two dimensions: firmsversus establishments and goods-producing versus service sectors.We summarize the decompositions; full results are available onrequest.

7.1 Establishment size

The only consistent break in the 1979 and 1993 series on estab-lishment size is at 100 employees, so we use this cut point to dis-tinguish large versus small establishments. The size distribution ofemployees has remained almost identical over this period, with asmall rise from 58.9 to 59.6 per cent in establishments employingunder 100 employees. The raw wage advantage of large establish-ments rose slightly from 29.1 to 30.6 per cent (log points, to beprecise). When we include standard controls (listed in Table A2), the



wage advantage of large establishments remains almost constant,declining from 10.5 to 10.4 per cent. Slowly rising raw gaps and con-stant regression-corrected gaps imply that larger establishmentshave been slowly gaining workers with high-wage characteristics.

We can see that result more carefully with the decomposition ofobservable worker characteristics and wages over time. Each com-ponent of the between-establishment decomposition (see Table 5,column 2) is of the same sign as the between-firm analysis (see Table5, column 1). Specifically, returns at large and small establishmentshave converged slightly (part (A)), characteristics at large establish-ments have converged with those at small firms (term B < 0), returnshave risen on average for characteristics present at large establish-ments (term C > 0), and large establishments increasingly hireemployees with characteristics for which such large establishmentspay high wages (term D > 0). All but the last effect is much smallerthan for the decomposition of the firm-size effect (and the last termwas already small). The net result, due largely to slower convergenceof characteristics, is the small divergence of wages for observablysimilar people between large and small establishments; this result isin contrast to the convergence between large and small firms.

The total establishment effect is a combination of the gapbetween small establishments in large and small firms and betweenlarge and small establishments within large firms. (As we use a cutpoint of 100 employees to define both a small firm and small estab-lishment, by definition there are no large establishments at smallfirms.) The gap between small establishments in large firms andsmall firms (see Table 5, column 4) fell substantially, by 20.9 per-centage points, between 1979 and 1993. Three of the four com-ponents of the decomposition are negative; component B isparticularly large in magnitude. In net, small establishments in largefirms became more like ‘small establishments’ in small firms, or,more accurately, like small firms.

In contrast, the gap between large and small establishments inlarge firms widened by 15.7 percentage points (see Table 5, column3). All components were positive, suggesting a large change in paystructures and employment structures within the large firm sector.In combination with the column 4 results, this suggests that thecohesion of large-firm pay structures broke down between 1979 and1993; employees in small establishments were no longer being paidas if they were employees of a large firm.

These results also suggest some limits to our illustrative model.Recall that in our illustrative model the effect of microcomputers





Tab

le 5

.E

stab

lishm

ents

ver

sus

firm

s(c

ombi

ned

1979

and

199

3 ba

se) Siz

e–w

age

gap

com

pone

nts

Sm

all e

stab

lishm

ents

L

arge

ver

sus

smal

lat

larg

e fir

ms

vers

usL

arge

ver

sus

Lar

ge v

ersu

s sm

all

esta

blis

hmen

tssm

all e

stab

lishm

ents

Des

crip

tion

of

size

–wag

esm

all fi

rms

esta

blis

hmen

tsw

ithi

n la

rge

firm

sat

sm

all fi

rms

com

pone

nt1

23

4

AH

ave

retu

rns

at la

rge

wor

kpla

ces

-0.0

79-0

.016

0.03

9-0

.066

dive

rged

fro

m s

mal

l wor

kpla

ces?

BH

ave

char

acte

rist

ics

at la

rge

-0.1

24-0

.041

0.04

0-0

.149

wor

kpla

ces

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rged

fro

m s

mal

lw

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lace

s?C

Hav

e re

turn

s ri

sen

on a

vera

ge f

or

0.07

70.

051

0.02

50.

019

empl

oyee

s at

larg

e w

orkp

lace

s?D

Do

larg

e w

orkp

lace

s in

crea

sing

ly

0.01

20.

021

0.05

09-0

.013

hire

em

ploy

ees w

ith

char

acte

rist

ics

that

larg

e w

orkp

lace

s re

war

d?

Sum

(i.e

.cha

nge

in t

he s

ize–

wag

e -0

.114

0.01

50.

157

-0.2

09ef

fect

)

Not

es:

Row

s A

–D a

re d

efine

d in

equ

atio

n [1

];no

te t

hat

in c

olum

n 1

wor

kpla

ces

are

firm

s,w

hile

in

colu

mns

2–4

wor

kpla

ces

are

esta

blis

hmen

ts.

Eac

h co

lum

n us

es a

diff

eren

t sa

mpl

e.C

olum

n 1

is a

n es

tim

ate

com

bini

ng t

he 1

979

and

1993

res

ults

rep

orte

d in

Tab

le 4

usi

ng e

qual

wei

ghts

.C

olum

n 2

exam

ines

lar

ge (

over

100

) an

d sm

all

esta

blis

hmen

ts.

Col

umn

3 ex

amin

es l

arge

and

sm

all

esta

blis

hmen

ts,

but

only

wit

hin

larg

efir

ms

(ove

r 10

0 em

ploy

ees)

.Col

umn

4 co

mpa

res

smal

l est

ablis

hmen

ts a

t la

rge

vers

us s

mal

l firm

s.

between firms and between establishments at large firms should beidentical — lower prices for microcomputers make it cost-effectiveto put technology (and, thus, more highly skilled workers) in smallerworkplaces. The shift of workers with high-wage characteristics outof big firms was not matched by a flow out of big establishmentsto small establishments at big firms. That is, in Table 5, column 3;row B, the term measuring difference in employee characteristicsacross establishment sizes, is now a small positive, while it is a largenegative number across firms. This result casts doubt on the hypoth-esis that microcomputers or another size-biased, skill-biased shockexplains our results.

7.2 Goods-producing versus service industries

Decomposition results are also of the same sign as overall butgenerally attenuated if we focus only on the goods-producing sector(see Table 6, column 2). The key difference is much smaller con-vergence of the characteristics at large and small firms in this sectorthan in services. The result is that the size–wage gap has risenslightly in goods-producing firms, while it has fallen strongly over-all. The differences between the findings for the goods-producingand service sectors may be taken as a warning against economy-wide generalizations; the impact of factors such as computers onindustries may be specific rather than general, reflecting differencesin technologies as well as other circumstances.

Davis and Haltiwanger (1991) report an increase in the size–wageeffect for manufacturing establishments while we report a decreasefor the firm-size effect in the entire private sector. Both sets of resultsare important. When we use our method to examine changes inwage gaps across manufacturing establishments our results aresimilar to theirs (see Table 6, column 4). Specifically, returns toemployee characteristics have diverged slightly across large andsmall manufacturing establishments (the same sign, though of asmaller magnitude than found by Davis and Haltiwanger). There isno specific theory that posits this pattern of results.

7.3 Robustness checks

We performed a few additional robustness checks (results areavailable on request). The results are as expected for medium-sizedfirms (100 to 1,000 employees), with changes the same size as butsmaller than the changes between the changes between small and





Tab

le 6

.G

oods

-pro

duci

ng v

ersu

s se

rvic

e in

dust

ries

(co

mbi

ned

1979

and

199

3 ba

se)

Siz

e–w

age

gap

com

pone

nts

All

Goo

ds-p

rodu

cing

Ser

vice

-sec

tor

Goo

ds-p

rodu

cing

firm

sfir

ms

firm

ses

tabl

ishm

ents

12

34

AH

ave

retu

rns

at la

rge

wor

kpla

ces

-0.0

79-0

.080

-0.0

72-0

.012

dive

rged

fro

m s

mal

l wor

kpla

ces?

BH

ave

char

acte

rist

ics

at la

rge

-0.1

24-0

.079

-0.1

05-0

.061

wor

kpla

ces

dive

rged

fro

m s

mal

lw

orkp

lace

s?C

Hav

e re

turn

s ri

sen

on a

vera

ge f

or0.

077

0.15

0.04

00.

063

empl

oyee

s at

larg

e w

orkp

lace

s?D

Do

larg

e w

orkp

lace

s in

crea

sing

ly h

ire

0.01

20.

052

0.00

10.

035

empl

oyee

s w

ith

char

acte

rist

ics

that

larg

e w

orkp

lace

s re

war

d?

Sum

(i.e

.cha

nge

in t

he s

ize–

wag

e-0

.114

0.04

9-0

.135

510.

025

effe

ct)

Not

es:

Row

s A

–D a

re d

efine

d in

equ

atio

n [1

];no

te t

hat

in c

olum

ns 1

–3 w

orkp

lace

s ar

e fir

ms,

whi

le i

n co

lum

n 4

wor

kpla

ces

are

esta

blis

hmen

ts.

Eac

h co

lum

n us

es a

diff

eren

t sa

mpl

e.C

olum

n 1

is t

aken

fro

m T

able

4,

‘Siz

e–w

age

gap’

.C

olum

n 4

exam

ines

the

siz

e–w

age

gap

amon

g es

tabl

ishm

ents

in m

anuf

actu

ring

;the

oth

er c

olum

ns e

xam

ine

gaps

am

ong

firm

s.

large firms. The results are also similar if we choose 1979 or 1993as a base year, instead of our use of an average of the two.

8. Discussion

The forces underlying the large-firm advantage in wages haveremained a topic of discussion and research for more than half acentury. One view argues that large firms are better able to usehighly skilled workers. The observed wage advantage of large firmsis an outcome of both large firms’ greater use of more highly skilledworkers (sorting) and the fact that large firms generate largerreturns to those workers. As not all of the productivity-related traitsare observable, a regression will leave some part of the skill-relatedreturns attributed to firm size.

The emerging stylized facts on returns to skill and size challengethis view. Rising returns to observed skills have been well docu-mented. Any model of rising returns to skill implies that returns toobservable skills such as age and education rose (hypothesis 1). Ifsize is proxying for skills and skills are sorted by firm size, returnsshould have risen for characteristics disproportionately present atlarge firms (hypothesis 4). Consistent with such findings and thehypothesis that firm size proxies for skill, large firms continue topay more than small firms. Running counter to this view, however,the pay advantage of large firms has declined over the past twodecades even as returns to skills have risen.

This article examines this issue through a decomposition of May1979 and April 1993 CPS data by firm size and year. If technologi-cal change affects large and small firms similarly, then the decom-position of these data does not support the view that firm sizeproxies for skills. Although there is evidence that returns for char-acteristics common at large firms are rising, we find substantial con-vergence in the returns and characteristics of large and small firms.These results are only with regard to observed characteristics, butit is unlikely that observed and unobserved characteristics andreturns would move in opposite directions.

One possible explanation for this divergence from the ‘size asskills’ hypothesis is that while skill-biased technological change hasproceeded over this period, it has been biased toward smaller firms.Had technological change been size neutral or biased toward largerfirms we would have expected to observe an increasing concentra-tion of highly skilled workers at large firms (hypothesis 2A) and a



larger gap between the wages of large and small firms (hypothesis3A). As noted, we find no evidence of either trend. However, whentechnological change is biased toward single-plant firms, we expectthat highly skilled workers will be less concentrated in large firms(hypothesis 2B) and the wage gap between large and small firms willdecrease (hypothesis 3B). This outcome is consistent with the neg-ative shifts in the first two elements of our decomposition. It is alsoconsistent with shifts in some of the important sub-components ofthese elements. The gaps in tenure, age, and percent female have allnarrowed, as has the gap in the percentage of union members inlarge and small firms. The characteristics that most directly measurehuman capital — age and education — remained essentially stable.

Taken as a whole, our result suggests that the reduction in thecosts of computing since 1979 may have substantially reduced thehistoric economies of scale in technology use enjoyed by multi-establishment firms. This size-biased and skill-biased technologicalchange, in turn, has resulted in a narrowing of the differences in thecharacteristics of the labor forces of large and small firms, in thereturns to characteristics of those labor forces, and in the wagesearned by the employees in large and small firms.

At the same time, these patterns do not show up in goods-producing sectors (where the size–wage gap has been fairly flat) orbetween large and small establishments at large firms. Thus, nosingle story appears consistent with all the patterns we observe. Itmay be that technology, or its impact, is not homogeneous bysector. It may be that goods-producing and service industries usedifferent types of computers or information technologies, that the effect of these technologies is quite different, or that the speedof the effect differs by industry. More disaggregate examination orexamination over a longer period may provide further insights intothe relationship between skills, size and compensation and how thisis changing over time.



Appendix



Table A1. Sectoral distribution of employment by firm size

1979 1993

Distribution of Distribution ofemployment employment

Industry No. of obs (as proportion) No. of obs (as proportion)

Mining 165 1131,000 plus 0.694 0.479100–999 0.173 0.277Under 100 0.133 0.244

Construction 758 6121,000 plus 0.101 0.106100–999 0.171 0.157Under 100 0.728 0.737

Non-durables 1,418 1,1981,000 plus 0.532 0.537100–999 0.240 0.233Under 100 0.227 0.240

Durable goods 2,364 1,5971,000 plus 0.652 0.567100–999 0.177 0.234Under 100 0.172 0.199

Transportation 535 5761,000 plus 0.523 0.569100–999 0.339 0.132Under 100 0.138 0.299

Communications 243 2041,000 plus 0.806 0.789100–999 0.075 0.101Under 100 0.118 0.110

Utilities 160 1521,000 plus 0.774 0.721100–999 0.124 0.147Under 100 0.102 0.131

Wholesale trade 645 6251,000 plus 0.249 0.284100–999 0.246 0.248Under 100 0.505 0.468

Retail trade 2,396 2,4941,000 plus 0.313 0.465100–999 0.123 0.118Under 100 0.565 0.417

Finance, insurance, etc. 916 1,0201,000 plus 0.430 0.524100–999 0.187 0.189Under 100 0.384 0.288



Table A1. Continued

1979 1993

Distribution of Distribution ofemployment employment

Industry No. of obs (as proportion) No. of obs (as proportion)

Service industries 428 5361,000 plus 0.187 0.323100–999 0.113 0.176Under 100 0.700 0.501

Professional services 1,767 2,4881,000 plus 0.228 0.327100–999 0.264 0.252Under 100 0.509 0.421

Table A2. Distribution of employment by establishment size

Establishment size 1979 (%) 1993 (%)

Under 25 36.7 33.225–99 24.0 25.5100 plus 39.3 41.3

Table A3. Establishment size effects on wages: 1979–93

1979 1993

Real (1993 dollars) wage by establishment sizeUnder 25 employees $10.43 $9.9425–99 employees $11.88 $11.40Gap in log wage over small firm wage 13.9% 14.7%100 or more employees $14.13 $13.69Gap in log wage over small firm wage 35.5% 37.7%

Regression estimates of medium- and large-firm effects on log(wage) (t-statistics in parentheses)

25–99 0.0645 0.035(6.5) (3.7)

100 plus 0.154 0.111(14.9) (12.2)

Notes: Control variables are listed in Table A4. Small establishments (<25) are the omittedcategory. Deflation uses the CPI-U-X1. Note that large establishments have 100 ormore employees, while large firms have 1,000 or more employees.



Tab

le A

4.C

oeffi

cien

ts a

nd g

ap in

larg

e- a

nd s

mal

l-fir

m c

oeffi

cien

ts,1

979–

93

1979

coe

ffici

ents

1993

coe

ffici

ents

Lar

ge fi

rmS

mal

l firm

Lar

ge fi

rmS

mal

l firm

Cha

nge

in t

he g

ap

Coe

ff.

tC

oeff

.t

Coe

ff.

tC

oeff

.t

Dif

fere

nce

t

Con

stan

t2.

3392

73.3

2.12

0362

.81.

9902

60.6

1.97

2050

.1-0

.201

-2.9

Edu

cati

on0.

0403

16.6

0.02

9511

.30.

0544

16.6

0.05

8019

.0-0

.014

-2.5

Edu

cati

on2

0.00

143.

0-0

.000

2-0

.40.

0044

6.4

0.00

274.

00.

000

0.2

Age

0.00

538.

90.

0056

10.2

0.00

659.

90.

0074

10.8

-0.0

01-0

.4A

ge2

-0.0

003

-9.9

-0.0

004

-15.

0-0

.000

4-1

1.3

-0.0

003

-9.5

-0.0

00-2

.2T

enur

e0.

0135

9.5

0.01

005.

70.

0197

13.6

0.01

286.

50.

003

1.0

Ten

ure2

-0.0

003

-4.7

-0.0

001

-1.0

-0.0

004

-6.3

-0.0

002

-2.3

0.00

00.

1T

enur

e <1

yea

r-0

.040

6-2

.4-0

.039

9-2

.3-0

.065

4-3

.4-0

.072

9-3

.50.

008

0.2

Ten

ure

1–2

year

s-0

.004

3-0

.2-0

.051

0-2

.5-0

.025

0-1

.0-0

.037

7-1

.5-0

.034

-0.8

Mar

ried

0.04

764.

20.

0544

4.2

0.05

624.

80.

0493

3.5

0.01

40.

5U

nion

0.05

544.

50.

2391

11.9

0.10

637.

10.

2352

7.6

0.05

51.

3B

lack

-0.0

463

-2.7

-0.0

825

-3.9

-0.0

671

-4.0

-0.0

853

-3.3

-0.0

18-0

.4F

emal

e-0

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3-2

0.3

-0.2

618

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2-0

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1-1

1.1

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113

-13.

70.

063

2.3

Met

ropo

litan

0.07

606.

50.

0831

6.6

0.12

489.

00.

1391

9.3

-0.0

07-0

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orth

east

-0.0

673

-4.5

-0.0

374

-2.2

-0.0

063

-0.4

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690

-3.6

0.09

32.

7N

orth

Cen

tral

-0.0

535

-3.6

-0.0

365

-2.1

-0.0

668

-4.4

-0.1

341

-7.4

0.08

42.

6



Sout

h-0

.109

5-7

.0-0

.088

5-5

.2-0

.079

5-5

.3-0

.146

1-8

.20.

088

2.7

Man

ager

0.27

129.

70.

3271

10.5

0.32

5510

.60.

3334

8.8

0.04

80.

8P

rofe

ssio

nal

0.22

437.

60.

2055

5.6

0.30

399.

40.

1845

4.5

0.10

11.

4T

echn

ical

0.10

252.

90.

3072

4.9

0.22

636.

40.

2665

5.3

0.16

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7Sa

les

0.10

683.

50.

2124

6.7

0.15

475.

40.

2054

5.6

0.05

50.

9C

leri

cal

0.01

450.

60.

1165

3.9

0.05

732.

00.

1361

3.7

0.02

30.

4P

rote

ctiv

e0.

0140

0.2

-0.2

549

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0.10

801.

3-0

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7-0

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.106

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Serv

ice

occ.

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050

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558

-1.9

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627

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576

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0.04

40.

7C

raft

0.09

613.

80.

1942

7.0

0.15

645.

20.

1436

4.0

0.11

11.

9O

pera

tive

0.02

401.

00.

0557

1.8

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182

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579

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0.07

11.

1T

rans

port

.ope

rati

ve-0

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2.4

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7314

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3459

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0.29

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Non

-dur

able

mfg

0.20

0710

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1746

6.9

0.29

2813

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1691

5.3

0.09

82.

0D

urab

le m

fg0.

2685

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7-0

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Tra

nspo

rt.i

nd.

0.38

1315

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1250

3.7

0.41

2716

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1733

4.7

-0.0

17-0

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omm

unic

atio

ns0.

2673

9.6

0.28

914.

00.

2939

9.1

0.16

061.

80.

155

1.3

Uti

litie

s0.

2590

7.9

0.23

682.

50.

3977

10.4

0.38

434.

1-0

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-0.1

Who

lesa

le0.

2978

10.4

0.22

899.

40.

3271

10.8

0.23

358.

30.

025

0.4

FIR

E0.

2046

9.6

0.24

8410

.40.

2918

13.7

0.28

099.

60.

055

1.1

Serv

ice

ind.

0.01

230.

30.

0945

3.8

-0.0

016

-0.1

0.07

632.

70.

004

0.1

Pro

f.se

rv.

0.14

256.

50.

1751

9.1

0.18

018.

80.

2312

10.8

-0.0

18-0

.4



Tab

le A

4a.

Par

t A

:Are

ret

urns

con

verg

ing

betw

een

larg

e an

d sm

all fi

rms?

Cal

cula

tion

usi

ng 1

979

char

acte

rist

ics

Cal

cula

tion

usi

ng 1

993

char

acte

rist

ics

XS 79

Exc

ess

Bd(

exce

ss B

)* X

S 79X

S 93E

xces

s B

d(ex

cess

B)*

XS 93

Con

stan

t1.

0000

-0.2

007

-0.2

007

1.00

00-0

.200

7-0

.200

7E

duca

tion

-0.1

092

-0.0

144

0.00

160.

7129

-0.0

144

-0.0

103

Edu

cati

on2

7.66

960.

0002

0.00

186.

5427

0.00

020.

0016

Age

-0.5

075

-0.0

005

0.00

030.

8517

-0.0

005

-0.0

004

Age

222

5.47

7-0

.000

2-0

.033

916

6.19

98-0

.000

2-0

.025

0T

enur

e-2

.458

90.

0034

-0.0

084

-2.0

808

0.00

34-0

.007

1T

enur

e253

.242

50.

0000

0.00

0444

.878

70.

0000

0.00

04T

enur

e <1

yea

r0.

3174

0.00

820.

0026

0.24

890.

0082

0.00

20T

enur

e 1–

2 ye

ars

0.11

71-0

.034

0-0

.004

00.

0949

-0.0

340

-0.0

032

Mar

ried

0.57

730.

0137

0.00

790.

5705

0.01

370.

0078

Uni

on0.

0952

0.05

480.

0052

0.04

840.

0548

0.00

27B

lack

0.07

90-0

.018

1-0

.001

40.

0687

-0.0

181

-0.0

012

Fem

ale

0.46

490.

0626

0.02

910.

4894

0.06

260.

0307

Met

ropo

litan

0.71

16-0

.007

1-0

.005

10.

7443

-0.0

071

-0.0

053

Nor

thea

st0.

2399

0.09

260.

0222

0.19

530.

0926

0.01

81N

orth

Cen

tral

0.27

590.

0843

0.02

330.

2610

0.08

430.

0220

Sout

h0.

3134

0.08

760.

0275

0.30

810.

0876

0.02

70M

anag

er0.

1026

0.04

810.

0049

0.11

860.

0481

0.00

57



Pro

fess

iona

l0.

0693

0.10

060.

0070

0.09

590.

1006

0.00

97T

echn

ical

0.00

960.

1645

0.00

160.

0287

0.16

450.

0047

Sale

s0.

0896

0.05

490.

0049

0.13

690.

0549

0.00

75C

leri

cal

0.17

660.

0232

0.00

410.

1588

0.02

320.

0037

Pro

tect

ive

0.00

10-0

.106

2-0

.000

10.

0024

-0.1

062

-0.0

003

Serv

ice

occ.

0.19

230.

0441

0.00

850.

1813

0.04

410.

0080

Cra

ft0.

1604

0.11

090.

0178

0.12

440.

1109

0.01

38O

pera

tive

0.09

780.

0714

0.00

700.

0595

0.07

140.

0042

Tra

nspo

rt.o

p.0.

0467

0.09

450.

0044

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0945

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inin

g0.

0039

0.02

400.

0001

0.00

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0240

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onst

ruct

ion

0.11

22-0

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1-0

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20.

1077

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-0.0

118

Non

-dur

able

mfg

0.06

780.

0976

0.00

660.

0640

0.09

760.

0062

Dur

able

mfg

0.08

54-0

.005

5-0

.000

50.

0741

-0.0

055

-0.0

004

Tra

nspo

rt.i

nd.

0.03

58-0

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0-0

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60.

0405

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170

-0.0

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Com

mun

icat

ions

0.00

570.

1551

0.00

090.

0053

0.15

510.

0008

Uti

litie

s0.

0033

-0.0

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0.00

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8-0

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hole

sale

0.06

660.

0246

0.00

160.

0673

0.02

460.

0017

Fin

ance

etc

.0.

0691

0.05

470.

0038

0.06

770.

0547

0.00

37Se

rvic

e in

d.0.

0590

0.00

420.

0002

0.06

270.

0042

0.00

03P

rof.

serv

.0.

1746

-0.0

184

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0.23

09-0

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4-0

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3

Not

es:

Exc

ess

B=

Coe

ff.

esti

mat

ed o

n sa

mpl

e fr

om l

arge

firm

s —

Coe

ff.

Est

imat

ed o

n a

sam

ple

from

sm

all

firm

s.E

duca

tion

,ag

e an

d te

nure

are

cent

ered

to

have

mea

n =

0 in

the

ent

ire

sam

ple.

Om

itte

d oc

cupa

tion

is la

bore

r,re

gion

is W

est,

and

indu

stry

is r

etai

l tra

de.



Tab

le A

4b.

Par

t B

:Are

em

ploy

ee c

hara

cter

isti

cs c

onve

rgin

g be

twee

n la

rge

and

smal

l firm

s?

Cal

cula

tion

usi

ng 1

979

coef

ficie

nts

Cal

cula

tion

usi

ng 1

993

coef

ficie

nts

Exc

ess

XS

bS 79P

rodu

ctE

xces

s X

SbS 93

Pro

duct

Con

stan

t0.

0000

2.12

030.

0000

0.00

001.

9720

0.00

00E

duca

tion

-0.0

931

0.02

95-0

.002

7-0

.093

10.

0580

-0.0

054

Edu

cati

on2

1.75

86-0

.000

2-0

.000

31.

7586

0.00

270.

0047

Age

-0.5

961

0.00

56-0

.003

3-0

.596

10.

0074

-0.0

044

Age

237

.208

9-0

.000

4-0

.015

637

.208

9-0

.000

3-0

.012

9T

enur

e-0

.700

30.

0100

-0.0

070

-0.7

003

0.01

28-0

.008

9T

enur

e2-5

.519

9-0

.000

10.

0004

-5.5

199

-0.0

002

0.00

12T

enur

e <1

yea

r0.

0475

-0.0

399

-0.0

019

0.04

75-0

.072

9-0

.003

5T

enur

e 1–

2 ye

ars

0.00

39-0

.051

0-0

.000

20.

0039

-0.0

377

-0.0

001

Mar

ried

-0.0

566

0.05

44-0

.003

1-0

.056

60.

0493

-0.0

028

Uni

on-0

.100

40.

2391

-0.0

240

-0.1

004

0.23

52-0

.023

6B

lack

0.04

76-0

.082

5-0

.003

90.

0476

-0.0

853

-0.0

041

Fem

ale

0.09

14-0

.261

8-0

.023

90.

0914

-0.2

113

-0.0

193

Met

ropo

litan

-0.0

007

0.08

31-0

.000

1-0

.000

70.

1391

-0.0

001

Nor

thea

st-0

.030

5-0

.037

40.

0011

-0.0

305

-0.0

690

0.00

21N

orth

Cen

tral

-0.0

237

-0.0

365

0.00

09-0

.023

7-0

.134

10.

0032

Sout

h0.

0628

-0.0

885

-0.0

056

0.06

28-0

.146

1-0

.009

2



Man

ager

-0.0

107

0.32

71-0

.003

5-0

.010

70.

3334

-0.0

036

Pro

fess

iona

l-0

.021

40.

2055

-0.0

044

-0.0

214

0.18

45-0

.004

0T

echn

ical

-0.0

006

0.30

72-0

.000

2-0

.000

60.

2665

-0.0

002

Sale

s0.

0428

0.21

240.

0091

0.04

280.

2054

0.00

88C

leri

cal

0.00

120.

1165

0.00

010.

0012

0.13

610.

0002

Pro

tect

ive

-0.0

021

-0.2

549

0.00

05-0

.002

1-0

.054

70.

0001

Serv

ice

occ.

0.04

09-0

.055

8-0

.002

30.

0409

-0.0

576

-0.0

024

Cra

ft-0

.021

50.

1942

-0.0

042

-0.0

215

0.14

36-0

.003

1O

pera

tive

-0.0

480

0.05

57-0

.002

7-0

.048

0-0

.057

90.

0028

Tra

nspo

rt.o

p.0.

0066

0.08

540.

0006

0.00

660.

0178

0.00

01M

inin

g-0

.013

80.

3481

-0.0

048

-0.0

138

0.40

49-0

.005

6C

onst

ruct

ion

0.00

170.

3273

0.00

060.

0017

0.29

170.

0005

Non

-dur

able

mfg

-0.0

325

0.17

46-0

.005

7-0

.032

50.

1691

-0.0

055

Dur

able

mfg

-0.1

309

0.21

61-0

.028

3-0

.130

90.

2907

-0.0

380

Tra

nspo

rt.i

nd.

0.00

480.

1250

0.00

060.

0048

0.17

330.

0008

Com

mun

icat

ions

-0.0

066

0.28

91-0

.001

9-0

.006

60.

1606

-0.0

011

Uti

litie

s-0

.004

80.

2368

-0.0

011

-0.0

048

0.38

43-0

.001

8W

hole

sale

0.00

060.

2289

0.00

010.

0006

0.23

350.

0001

FIR

E0.

0277

0.24

840.

0069

0.02

770.

2809

0.00

78Se

rvic

e in

d.0.

0148

0.09

450.

0014

0.01

480.

0763

0.00

11P

rof.

serv

.0.

0172

0.17

510.

0030

0.01

720.

2312

0.00

40

Not

e:E

xces

s X

=m

ean

from

larg

e-fir

m s

ampl

e fir

ms

mea

n fr

om s

mal

l-fir

m s

ampl

e.



Tab

le A

4c.

Par

t C

:Are

ret

urns

ris

ing

for

char

acte

rist

ics

com

mon

at

larg

e fir

ms?

1979

bas

e19

93 b

ase

(XL 79

-X

S 79)

(bL 93

-bL 79

)P

rodu

ct(X

L 93-

XS 93

)(b

L 93-

bL 79)

Pro

duct

Con

stan

t0.

0000

-0.3

490

0.00

000.

0000

-0.3

490

0.00

00E

duca

tion

0.79

670.

0141

0.01

130.

7036

0.01

410.

0100

Edu

cati

on2

-1.1

505

0.00

31-0

.003

60.

6082

0.00

310.

0019

Age

1.05

460.

0012

0.00

130.

4585

0.00

120.

0006

Age

2-6

3.66

61-0

.000

10.

0050

-26.

4572

-0.0

001

0.00

21T

enur

e4.

3316

0.00

620.

0269

3.63

130.

0062

0.02

26T

enur

e238

.796

2-0

.000

1-0

.005

533

.276

3-0

.000

1-0

.004

7T

enur

e <1

yea

r-0

.153

9-0

.024

80.

0038

-0.1

064

-0.0

248

0.00

26T

enur

e 1–

2 ye

ars

-0.0

384

-0.0

207

0.00

08-0

.034

5-0

.020

70.

0007

Mar

ried

0.08

660.

0086

0.00

070.

0300

0.00

860.

0003

Uni

on0.

2439

0.05

090.

0124

0.14

350.

0509

0.00

73B

lack

0.00

32-0

.020

8-0

.000

10.

0508

-0.0

208

-0.0

011

Fem

ale

-0.1

200

0.11

32-0

.013

6-0

.028

60.

1132

-0.0

032

Met

ropo

litan

0.06

040.

0488

0.00

290.

0597

0.04

880.

0029

Nor

thea

st0.

0342

0.06

100.

0021

0.00

370.

0610

0.00

02N

orth

Cen

tral

0.03

51-0

.013

3-0

.000

50.

0114

-0.0

133

-0.0

002

Sout

h-0

.052

80.

0300

-0.0

016

0.01

000.

0300

0.00

03



Man

ager

0.01

770.

0543

0.00

100.

0070

0.05

430.

0004

Pro

fess

iona

l0.

0417

0.07

960.

0033

0.02

020.

0796

0.00

16T

echn

ical

0.02

010.

1238

0.00

250.

0194

0.12

380.

0024

Sale

s-0

.029

50.

0479

-0.0

014

0.01

330.

0479

0.00

06C

leri

cal

0.02

440.

0428

0.00

100.

0255

0.04

280.

0011

Pro

tect

ive

0.00

400.

0940

0.00

040.

0019

0.09

400.

0002

Serv

ice

occ.

-0.1

293

0.04

23-0

.005

5-0

.088

40.

0423

-0.0

037

Cra

ft0.

0005

0.06

030.

0000

-0.0

209

0.06

03-0

.001

3O

pera

tive

0.07

67-0

.042

3-0

.003

20.

0287

-0.0

423

-0.0

012

Tra

nspo

rt.o

p.-0

.014

30.

0269

-0.0

004

-0.0

077

0.02

69-0

.000

2M

inin

g0.

0172

0.08

080.

0014

0.00

350.

0808

0.00

03C

onst

ruct

ion

-0.0

961

-0.1

447

0.01

39-0

.094

4-0

.144

70.

0137

Non

-dur

able

mfg

0.08

660.

0921

0.00

800.

0541

0.09

210.

0050

Dur

able

mfg

0.23

830.

0692

0.01

650.

1074

0.06

920.

0074

Tra

nspo

rt.i

nd.

0.02

110.

0314

0.00

070.

0258

0.03

140.

0008

Com

mun

icat

ions

0.03

410.

0266

0.00

090.

0275

0.02

660.

0007

Uti

litie

s0.

0223

0.13

870.

0031

0.01

750.

1387

0.00

24W

hole

sale

-0.0

328

0.02

93-0

.001

0-0

.032

20.

0293

-0.0

009

FIR

E0.

0105

0.08

710.

0009

0.03

830.

0871

0.00

33Se

rvic

e in

d.-0

.042

8-0

.013

90.

0006

-0.0

280

-0.0

139

0.00

04P

rof.

serv

.-0

.094

20.

0376

-0.0

035

-0.0

770

0.03

76-0

.002

9



Tab

le A

4d.

Par

t D

:Do

empl

oyee

s at

larg

e fir

ms

incr

easi

ngly

hav

e ch

arac

teri

stic

s th

at la

rge

firm

s re

war

d w

ell?

1979

cal

cula

tion

1993

cal

cula

tion

(bL 93

-bL 79

)(X

L 93-

XL 79

)P

rodu

ct(b

L 93-

bS 93)

(XL 93

-X

L 79)

Pro

duct

Con

stan

t0.

2189

0.00

000.

0000

0.01

820.

0000

0.00

00E

duca

tion

0.01

080.

7290

0.00

79-0

.003

60.

7290

-0.0

026

Edu

cati

on2

0.00

150.

6317

0.00

100.

0018

0.63

170.

0011

Age

-0.0

003

0.76

32-0

.000

2-0

.000

80.

7632

-0.0

006

Age

20.

0001

-22.

0692

-0.0

016

-0.0

001

-22.

0692

0.00

17T

enur

e0.

0035

-0.3

222

-0.0

011

0.00

69-0

.322

2-0

.002

2T

enur

e2-0

.000

2-1

3.88

370.

0029

-0.0

002

-13.

8837

0.00

28T

enur

e <1

yea

r-0

.000

7-0

.020

90.

0000

0.00

75-0

.020

9-0

.000

2T

enur

e 1–

2 ye

ars

0.04

67-0

.018

2-0

.000

90.

0127

-0.0

182

-0.0

002

Mar

ried

-0.0

068

-0.0

635

0.00

040.

0069

-0.0

635

-0.0

004

Uni

on-0

.183

7-0

.147

20.

0270

-0.1

289

-0.1

472

0.01

90B

lack

0.03

630.

0373

0.00

140.

0182

0.03

730.

0007

Fem

ale

0.01

550.

1159

0.00

180.

0781

0.11

590.

0091

Met

ropo

litan

-0.0

072

0.03

21-0

.000

2-0

.014

30.

0321

-0.0

005

Nor

thea

st-0

.029

9-0

.075

10.

0022

0.06

27-0

.075

1-0

.004

7N

orth

Cen

tral

-0.0

170

-0.0

386

0.00

070.

0673

-0.0

386

-0.0

026



Sout

h-0

.021

10.

0575

-0.0

012

0.06

650.

0575

0.00

38M

anag

er-0

.055

90.

0053

-0.0

003

-0.0

078

0.00

53-0

.000

0P

rofe

ssio

nal

0.01

880.

0052

0.00

010.

1195

0.00

520.

0006

Tec

hnic

al-0

.204

70.

0185

-0.0

038

-0.0

402

0.01

85-0

.000

7Sa

les

-0.1

056

0.09

02-0

.009

5-0

.050

70.

0902

-0.0

046

Cle

rica

l-0

.101

9-0

.016

60.

0017

-0.0

788

-0.0

166

0.00

13P

rote

ctiv

e0.

2689

-0.0

006

-0.0

002

0.16

27-0

.000

6-0

.000

1Se

rvic

e oc

c.-0

.049

20.

0299

-0.0

015

-0.0

051

0.02

99-0

.000

2C

raft

-0.0

981

-0.0

574

0.00

560.

0128

-0.0

574

-0.0

007

Ope

rati

ve-0

.031

6-0

.086

20.

0027

0.03

97-0

.086

2-0

.003

4T

rans

port

.op.

-0.0

865

0.00

85-0

.000

70.

0081

0.00

850.

0001

Min

ing

0.04

90-0

.012

6-0

.000

60.

0730

-0.0

126

-0.0

009

Con

stru

ctio

n0.

1633

-0.0

028

-0.0

005

0.05

42-0

.002

8-0

.000

2N

on-d

urab

le m

fg0.

0261

-0.0

362

-0.0

009

0.12

37-0

.036

2-0

.004

5D

urab

le m

fg0.

0524

-0.1

422

-0.0

074

0.04

69-0

.142

2-0

.006

7T

rans

port

.ind

.0.

2563

0.00

950.

0024

0.23

930.

0095

0.00

23C

omm

unic

atio

ns-0

.021

8-0

.007

00.

0002

0.13

33-0

.007

0-0

.000

9U

tilit

ies

0.02

21-0

.003

3-0

.000

10.

0133

-0.0

033

-0.0

000

Who

lesa

le0.

0689

0.00

130.

0001

0.09

360.

0013

0.00

01F

IRE

-0.0

438

0.02

64-0

.001

20.

0109

0.02

640.

0003

Serv

ice

ind.

-0.0

822

0.01

85-0

.001

5-0

.078

00.

0185

-0.0

014

Pro

f.se

rv.

-0.0

327

0.07

35-0

.002

4-0

.051

10.

0735

-0.0

038



Tab

le A

5.T

he g

ap in

cha

ract

eris

tics

,197

9–93

1979

mea

ns19

93 m

eans

Cha

nge

in t

he g

apL

arge

firm

Sm

all fi

rmL

arge

firm

Sm

all fi

rm(1

979–

93)

Mea

nt

Mea

nt

Mea

nt

Mea

nt

Dif

fere

nce

t

Edu

cati

on12

.687

535

7.5

11.8

937

297.

813

.416

538

6.7

12.7

129

1207

.8-0

.090

2-0

.1E

duca

tion

216

7.01

8910

31.8

149.

1125

682.

918

5.14

5912

92.0

167.

6523

640.

6-0

.412

8-0

.4A

ge36

.547

119

9.2

35.3

541

163.

237

.310

320

5.3

36.8

517

5372

.3-0

.734

4-0

.7A

ge2

1,49

7.20

0059

2.7

1,46

9.90

3039

5.7

1,53

0.08

2048

5.7

1,52

3.52

5015

,531

.1-2

0.74

00-4

.5T

enur

e8.

8727

65.3

4.49

4745

.38.

5505

95.1

4.91

9290

.6-0

.746

7-0

.7T

enur

e216

7.25

6465

.466

.072

836

.214

8.86

1897

.164

.747

451

.5-1

7.06

93-5

.2T

enur

e <1

yea

r0.

1635

30.6

0.31

7447

.20.

1425

23.3

0.24

8915

6.4

0.04

750.

0T

enur

e 1–

2 ye

ars

0.07

8720

.20.

1171

25.2

0.06

0514

.60.

0949

184.

00.

0039

0.0

Mar

ried

0.66

3997

.40.

5773

81.0

0.60

0585

.90.

5705

1271

.5-0

.056

6-0

.1U

nion

0.33

9149

.60.

0952

22.5

0.19

1963

.30.

0484

22.5

-0.1

004

-0.1

Bla

ck0.

0823

20.7

0.07

9020

.30.

1195

33.4

0.06

8790

.50.

0476

0.0

Fem

ale

0.34

4950

.30.

4649

64.6

0.46

0865

.30.

4894

1144

.50.

0914

0.1

Met

ropo

litan

0.77

2012

7.5

0.71

1610

8.8

0.80

4013

0.5

0.74

4383

3.0

-0.0

007

-0.0

Nor

thea

st0.

2741

42.6

0.23

9938

.90.

1990

35.5

0.19

5335

35.9

-0.0

305

-0.0

Nor

th C

entr

al0.

3111

46.6

0.27

5942

.80.

2725

43.9

0.26

1015

26.5

-0.0

237

-0.0



Sout

h0.

2606

41.1

0.31

3446

.80.

3181

48.8

0.30

8120

63.0

0.06

280.

1M

anag

er0.

1203

25.6

0.10

2623

.40.

1256

27.5

0.11

8611

35.9

-0.0

107

-0.0

Pro

fess

iona

l0.

1109

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Notes

1 To simplify the model we measure firm size as the number of establishments,not the size per establishment. Alternative models could assume that PCs reducethe fixed cost of information technology. In such a model computers are adoptedat smaller establishments and the highly skilled labor that is complementary tocomputers also shifts to smaller establishments. Thus, the main results of ourmodel would go through.

2 The coding of the employer size variable was altered in 1988 by a change inthe top coding of establishment size from 1,000 to 250. In both years, individualswere first asked the employment of the establishment in which they work, thenwhether they work for a multi-establishment firm and then, if they do, the employ-ment of the firm. All questions are reported as discrete categories. In 1979, estab-lishment size was top coded at 1,000 employees, but it was top coded at 250 in1993. As a result, there are a small number of individuals who worked in largesingle-establishment firms in 1993 who were classified as being in firms of 100 to499 employees rather than being properly recorded as working in firms of 500 to999 or 1,000 or more.

3 The CPS provides employment-weighted measures of employer size (a ‘whitepages’ view), rather than an employer-weighted measure (a ‘yellow pages’ view).Employment-weighted statistics result in a higher mean employment size and a firm size distribution more heavily weighted toward large firms. Employer-weighted estimates provide a lower mean and median and a distribution skewedtoward small firms because there are large numbers of extremely small firms in theUSA. Employer-weighted statistics are computed assigning smaller employers thesame weight (importance) as the largest employers.

4 The shift of employment toward larger firms is the reverse of prediction of thetheory that the introduction of PCs would result in a decline in the employmentsize of firms. The difference between a comparative static exercise and the worldmay be due to the multitude of factors other than those under study, which affectfirm size.

5 Changes in the interception associated with changing the omitted categoriesare largely balanced by corresponding shifts in the effect of personal, occupationand industry effects; changing the omitted group results in only modest changesin the contribution of part (A) of the decomposition to the size–wage gap or inthe overall size–wage gap.

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size, skill and sorting

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