CORPORATE DEMOGRAPHY AND WAGE INEQUALITY:

VERTICAL AND HORIZONTAL SORTING AS SOURCES OF REGIONAL WAGE DISPERSION*

Jesper B. Sørensen MIT Sloan School of Management

50 Memorial Drive, E52-581 Cambridge, MA 02142-1347

sorensen@mit.edu

Olav Sorenson UCLA Anderson Graduate School of Management

110 Westwood Plaza, Box 951481 Los Angeles, CA 90095-1481 osorenso@anderson.ucla.edu

September 2004

* We are indebted to Niels Westergaard-Nielsen and Tor Eriksson of the Aarhus School of Business for

allowing us to use the Pay and Performance data. Søren Leth-Sørensen, Jørn Hansen Schmidt, and Paul Bingeley were extremely helpful in facilitating access and providing time, advice and resources. We also thank Roberto Fernandez, Michael Hannan, Boyan Jovanovic, Leslie McCall, Glenn McDonald, Damon Phillips and Ezra Zuckerman for useful comments on earlier drafts of this paper. The usual disclaimer applies.

CORPORATE DEMOGRAPHY AND WAGE INEQUALITY: VERTICAL AND HORIZONTAL SORTING AS SOURCES OF REGIONAL WAGE DISPERSION

ABSTRACT

This study examines how wage inequality depends on corporate demography, or the number

and diversity of employers in a labor market. Drawing on insights from economics and

sociology, we identify two distinct theoretical mechanisms linking corporate demography to

wage inequality. One mechanism implies that wage dispersion should increase with the

number of firms competing for the same labor pool, as labor market competition drives

compensation to reflect worker heterogeneity. The second mechanism suggests that

organizational diversity should reduce inequality because it increases the odds that an

individual finds employment with a firm that can take advantage of his or her unique skills.

Our analysis of Danish census data provides support for each thesis: Within an industry, the

number of, and absence of concentration among, firms operating in a labor market increases

wage dispersion. The variety of industries offering employment within a region, however,

both reduces inequality and mitigates the effect of within-industry labor market competition.

1

How much money could a gifted shooting guard earn in a world with no

professional basketball teams? What would a gourmet chef earn in the absence of

restaurants? For both the basketball player and the chef, one can easily imagine that they

would earn less in such situations than they would if employers existed that desired their

distinctive traits. Though other organizations might value the shooting guard’s agility,

eye-hand coordination and physical stature, few, if any, would attach as much value to

the guard’s unique constellation of abilities and attributes as a basketball team. Similarly,

family and friends may appreciate the gourmet chef’s culinary creativity, senses of smell

and taste, and aesthetic talents, but firms that do not serve meals place less value on these

special talents than those that do. Denied access to their optimal lines of employment,

both the chef and the shooting guard would have to work in jobs that may not fit their

abilities particularly well. Moreover, they would potentially find themselves in

competition with others whose unique skills and characteristics do match those desired by

employers. The shooting guard, for example, might find a job with a baseball team, but

then will find himself in competition with others whose physical gifts make them

excellent baseball players. As a result, the shooting guard would likely earn less than he

would with a basketball team. (Michael Jordan’s inability to convert his basketball

success into a professional baseball career comes to mind.)

These hypothetical examples highlight the potential importance for income

inequality of the interaction between the distribution of individual abilities and attributes

in a labor market and the prevalence of employers with a need for such characteristics.

2

Most sociologists would consider uncontroversial the claim that wage differentials, to

some extent, reflect differences in individual characteristics. (Debate centers instead on

the extent to which wage differentials reflect productivity differences, as opposed to

echoing socially constructed beliefs about ability.) Other things being equal, basketball

teams compensate better the truly gifted basketball player than the less talented one, and

pay more for the taller player than the shorter one. The returns to possessing particular

abilities and attributes, however, depend on the match between individuals with those

qualities, on the one hand, and employers that can – or at least believe they can – make

effective use of them on the other (Sørensen, 1996: 1357). Michael Jordan’s fortunes

would decline in a world with baseball but no basketball teams; the chef without

restaurants as potential employers must settle for a second best outcome. Both have

specialized characteristics that they cannot capitalize through the labor market in the

absence of the right types of employers.

Some of these valued individual characteristics admittedly arise through

investments in training for particular roles. Human capital theories (Becker 1964), for

example, contend that rational individuals would not invest heavily in acquiring skills

that no employer wants. As the case of industrial restructuring suggests, however,

changes in the nature of employer demand can render past human capital investments

more or less valuable (Morris and Western 1999). Moreover, some differences in ability

arise from heterogeneity in traits that one might consider innate (e.g., height in the

context of basketball), in the sense that they do not stem from past investments in the

acquisition of particular skills. If one considers the distribution of individual abilities and

attributes at least partially exogenous to the labor market at a point in time, an important

3

sociological issue concerns the interaction between the distributions of these abilities and

attributes, and the social structure of the labor market, which determines their value.

Though some of these differences in demand from employers undoubtedly reflect real

individual productivity differences in a particular type of activity, others likely stem from

socially constructed beliefs about this relationship, as in the case of race and sex

discrimination. Regardless of the particular source of this variation in demand, however,

the allocation of rewards in society associated with a given distribution of characteristics

depends on the structure of the labor market, as individuals’ abilities and attributes meet

employers in this arena.

But what features of the labor market determine the value of these individual

characteristics? On the demand side, the labor market consists of formal organizations

that differ in a wide variety of ways. The intensity and nature of interactions between

these organizations determines the opportunities available to employees. Human and

organizational ecologists, in particular, have highlighted the degree of diversity embodied

in these formal organizations as an important determinant of community and industry

dynamics (e.g., Hawley, 1950; Hannan and Freeman, 1977). Recent organizational

research has begun to examine the linkages between labor market outcomes and the

corporate demography of labor markets – or the number and diversity of organizations

(employers) active in a particular labor market (Carroll and Hannan, 2000).1 For

example, a small number of studies have attempted to link the diversity and dynamics of

employers to individual career events, in terms of either promotion chances (Phillips,

2001), or mobility between employers (Greve, 1994; Haveman and Cohen, 1994).

1 We use “corporate demography” and “industrial demography” interchangeably.

4

Corporate demography may also influence other types of employment related

outcomes as well. In this paper, we draw on existing theory fragments in economics and

sociology to develop hypotheses regarding the influence of corporate demography on

wage dispersion. Our review of past theoretical work suggests two (seemingly

contradictory) expectations concerning the association between industry structure and

wage dispersion. The first account, drawing on economic models of the labor market,

maintains that (for fixed labor demand) a greater number of employers in a region should

increase wage inequality as firms increasingly diverge in their ability to employ human

capital effectively, thereby forcing wages to reflect underlying individual differences in

productivity (Lydall, 1959; Rosen, 1981; Wheeler, 2001). Returning to our example, the

larger the number of basketball teams, the greater the extent to which player salaries

should depend on differences in basketball ability. The second perspective, drawing on

arguments from organizational ecology, contends that wage dispersion should decline

with the number of organizations in the labor market, because workers have more

opportunities to match their characteristics to an employer in need of them (Hannan,

1988; see also Roy, 1951). In a world with only baseball teams, the athlete whose skills

match best the game of basketball will earn less than the player with skills ideally suited

to baseball, but in a world with both types of teams, inequality declines as the skills

related to basketball are more amply rewarded.

The differing predictions arise from a divergence in assumptions regarding the

nature of the labor market. Whereas most economic models of labor markets assume a

single dimension of worker quality, the ecological approach presupposes a multi-

dimensional world in which employees have diverse types of skills and organizations

5

have varying demands for them. If one assumes that organizations involved in similar

operations prefer employees with similar skills, income inequality should increase as the

number of such firms rises. On the other hand, organizations operating in different

industries frequently draw on disparate skill sets; hence, in the presence of heterogeneous

abilities and attributes, wage dispersion should decline with increasing diversity in the

industries represented in a local labor market. Moreover, the availability of these

opportunities should also allow employees to avoid working in industries in which they

could not contribute effectively (or in which they might face more severe discrimination),

thereby mitigating to some degree the salience of the number of firms within an industry

for income inequality.

We examine the relationship between corporate demography and income

inequality by analyzing regional variation in wage inequality as a function of regional

differences in corporate demography. Both within and across countries, income

inequality varies tremendously from one area to the next (Rauch, 1993; Blau and Kahn,

1996; McCall, 2000). We propose that differences in the corporate demography of the

local population of employers can help to explain this heterogeneity in inequality across

regions. We analyze comprehensive, yearly census data on the Danish population that

contains information on the geographic location of workplaces. Our results indicate that

local wage dispersion within an industry: (1) increases with the number of firms in the

industry, and (2) declines with the variety of employers available outside the industry.

The magnitude of the association between the number of firms and wage dispersion

(finding 1 above) also declines with the availability of employers outside the industry.

These results remain robust to a more conservative estimation approach using a two-stage

6

hierarchical linear model (Bryk and Raudenbush, 1992; McCall, 2000), where we first

control for all observable human capital effects on wages, and then examine the

relationship between industry structure and the residuals from these wage equations. Our

results therefore indicate that industrial demography, by shaping the local structure of

employment opportunities, plays an important role in determining inequality in the

distribution of wealth through wages.

CORPORATE DEMOGRAPHY AND INEQUALITY

Our analysis focuses not on the characteristics of individual firms, but rather on

the demography of the population of employers located in a particular region. In this

respect, our approach departs from most of the existing research on the role of

organizations in the stratification process, which has typically highlighted the dynamics

of internal labor markets (e.g., Barnett, Baron and Stuart, 2001), or the adoption of

particular human resource practices (e.g., Kalleberg et al., 1996). Though important to

our understanding of career trajectories, these perspectives have not considered explicitly

how these factors contribute to income inequality across the whole of society. In

principle, one could view this overall inequality as a simple aggregation of the underlying

characteristics of the organizations operating within it. Such an approach, however, fails

to consider the potential interactions among the firms that jointly determine labor market

dynamics (Carroll and Hannan, 2000). In particular, the perspective offered here

highlights the fact that labor market inequality results, in part, from the structure of

competition in the labor market, and that the diversity of organizations in a labor market

affects the dynamics of competition on the demand side of the labor market.

7

Although the vast majority of research on corporate demography has focused on

understanding how the characteristics of organizational populations influence both the

fates of individual firms and the evolution of industries, several studies suggest an

important link between corporate demography and labor market outcomes. In particular,

ecological dynamics appear to have a large effect on employee mobility. Examining the

movement of employees across firms, for example, Haveman and Cohen (1994)

demonstrate that workers most commonly leave their existing jobs either to join a newly

established firm or as a result of the dissolution of their employer; Carroll and Hannan

(2000: 430-431) estimate that such dynamics-related job shifts may account for as much

as 25% to 55% of all inter-firm employee mobility. Greve (1994; Fujikawa-Greve and

Greve, 2000) has further demonstrated that the rate of such shifts depends on the

demographic characteristics of a population – finding a positive relationship between

employee mobility and heterogeneity in the size distribution of firms. And recent studies

suggest that ecological processes influence not just the movement of employees across

firms, but also their upward mobility in internal labor markets; Phillips (2001; Phillips

and Sørensen, 2003) finds that employee promotion rates rise with an employer’s

susceptibility to ecological competition.

Our study builds on this ecological perspective, but considers the effects of

industrial demography with respect to a different type of labor market outcome, wage

inequality. Drawing on insights from the economics and sociological literatures, we

identify two seemingly inconsistent predictions concerning the relationship between the

diversity of the population of employers in a region and the degree of wage inequality.

The first, growing out of economic models of labor market competition, argues that more

8

intense competition should increase the dispersion in wage levels across workers (Lydall,

1959; Rosen, 1981; Wheeler, 2001). The second, building on the logic of human and

organizational ecology and focusing more on the opportunity structure available to

employees, argues that a wider variety of opportunities should reduce wage dispersion.

We discuss each approach in turn.

Competition, sorting and inequality

The traditional neoclassical approach to labor markets in economics contends that

firms pay workers their marginal product – in other words, each employee’s wage should

match the degree to which that individual contributes to the output of the firm. The logic

for this expectation rests on the assumption that firms will hire more employees if doing

so would increase their profits, and on the belief that employees choose to work for the

firm that offers them the highest wages. To the extent that wages reflect marginal

productivity, it then follows that wage inequality emerges from differences across

individuals in productivity.

Economic models of inequality offer a variety of accounts – differing in the extent

to which they emphasize heterogeneity among workers or heterogeneity among firms – of

the sources of this differential productivity. Traditional accounts focus on heterogeneity

in human capital, either as a consequence of variation in innate abilities or as the outcome

of differential investment in the acquisition of training and skills (Becker 1964). Since

such models typically assume homogeneity among firms, they do not imply a link

between industrial demography and inequality; firms with the same production

technology, regardless of their number, should benefit equally from hiring more

productive labor. An alternative approach assumes that firms differ in their ability to

9

capitalize on the talents of employees. Analytic models suggest that wage inequality can

arise even in the absence of heterogeneity across workers because equally skilled

employees might nonetheless differ in their productivity when employed in different

settings (e.g., using different technologies). Explanations along these lines have been

forwarded, for example, to explain the positive correlation observed between wages and

firm size (see Idson and Oi, 1999, for a review).

The more interesting approaches from our perspective, however, see inequality as

the result of a labor market matching process between heterogeneous employees and

heterogeneous employers (i.e., cases where both individuals and firms differ in

productivity or ability). One potential type of matching highlights the importance of the

scale or scope for the application of individual talents. A small difference in the abilities

of two individuals would normally only justify a small difference in their wages, though

production technologies might amplify this differential in absolute terms. But imagine

that markets differ in their sizes. In that case, one would expect a sorting of individuals to

markets, with the most talented individuals working in the largest markets and securing

the largest returns (Lydall, 1959; Rosen, 1981, 1982). To see the intuition behind this

effect, return to professional basketball. A more talented basketball player might increase

the probability that a potential fan buys a ticket to attend a game. In a small market, such

as Sioux Falls, South Dakota, with a population of about 100,000, the player might

increase expected ticket sales by 500, but the same small difference applied to the

Chicago market (roughly 60 times larger) could result in 30,000 additional tickets sold.

Hence, NBA basketball players differ only slightly in talent from those in the Continental

10

Basketball Association (CBA), but the two leagues offer dramatically different salary

scales.2

Though our presentation of this dynamic appears predicated on an assumption

that wages reflect underlying differences in worker ability, this type of sorting process

really only requires that firms have consistent beliefs – whether accurate or not – about

which employees they consider most valuable. Regardless of whether these differences

reflect actual heterogeneity in skill or simply perceived differences, this sorting dynamic

has been used to explain the highly skewed income distributions among artists and

athletes (Rosen, 1981), and among managers (Lydall, 1959; Rosen, 1982) – moving up

the corporate hierarchy or to larger firms allows the leveraging of managerial talents

across a broader range of operations.3 Greater heterogeneity in the scale or scope of

operations across firms would therefore lead one to expect more pronounced wage

inequality.

Another type of sorting argument depends not on the scale of operations (for a

particular type of activity) but on synergy between worker skill and the ability of an

employer to make effective use of that skill. In developing an analytical model to

understand the relationship between the number of employers, productivity and wage

inequality, Wheeler (2001) begins by assuming that one can array both employees and

employers along a single ‘quality’ dimension.4 Higher ability employees can produce

2 Television differentiates these two leagues even further by allowing the NBA to reach audiences

beyond the populations of the cities in which the games take place. 3 See Sattinger (1983) for a review. Since economists would typically expect competition to

remove inefficient allocations from the market, the stability of this equilibrium in economic models typically depends either on search costs (e.g., Albrecht, Axell and Lang, 1986) or on market power (e.g., Bhaskar, Manning and To, 2002).

4 Wheeler’s (2001) model has a nearly identical structure to that originally used by Becker (1973) to describe the matching of individuals in “marriage markets” and later by Kremer (1993) to explain the importance of the complementarities that result from highly skilled employees working with one another.

11

more, but the quality of the employer limits their effectiveness. For example, a highly

skilled chef might contribute positively to the profitability of a McDonalds restaurant, but

she could add far more value working for an employer that could utilize her skills more

effectively, such as a gourmet restaurant. In order of their quality (from highest to

lowest), firms in Wheeler’s model then search for employees.5 If they can search without

cost, the market generates a perfect quality match between employees and employers –

that is, firms match with employees of similar rank on the quality distribution (Becker,

1973). This perfect matching between employees and firms maximizes the expected level

of wage dispersion due to the higher productivity resulting from good matches. Search

costs introduce a friction that reduces the expected extent of this dispersion, but in either

case inequality increases with heterogeneity in the quality distribution of employers

(Kremer, 1993; Wheeler, 2001).

Organizational diversity and inequality

A very different perspective on the social implications of the number of

employers available arises from the literature on human and organizational ecology.

Ecologists assume that organizations in a community occupy more or less well-

differentiated niches, so that they survive by drawing on their own combinations of

resources from the environment (Hawley, 1950; Hannan and Freeman, 1977). In the labor

market, for example, some firms rely more heavily on employees with physical strength

and manual dexterity, while others rely on workers with strong analytic reasoning and

communication skills. Employees likewise have diverse sets of abilities and attributes. If

5 Though sequential search might seem unreasonable, one could think of it as being equivalent to a

situation in which workers choose to work for the highest quality firm when they receive more than one offer for employment.

12

these characteristics match well with the demands of their employer, workers receive

rewards in the form of bonuses, raises and internal promotion. A poor fit, on the other

hand, relegates them to lower pay and limited opportunities for advancement. In a world

with only one employer (or in which all employers look for the same types of

employees), one would expect substantial inequality as some individuals fit well to the

requirements of this organization and receive ample compensation, while others do not

(Hannan 1988). Moreover, those without the ‘right’ skills have little opportunity to

change employers; as Glaeser (1994: 19, quoted in Wheeler 2001) observes, “in a one-

company town, individuals who are imperfectly matched to that company have nowhere

else to go. These workers will stay at the company (or leave the town), being

underproductive.”

As the diversity of employers – and consequently the variety of the employee

abilities and attributes they desire – increases, inequality should decline because a larger

proportion of the population can find employers that desire their characteristics, leaving

few un- or under-employed. In a conceptual piece discussing the implications of this idea,

Hannan (1988) highlights the likely importance of three dimensions of the industrial

population: the number of firms, their variation in ages and their differences in size. To

the extent that firms occupy distinct niches, increasing numbers of firms should reduce

inequality because each firm prefers employees with somewhat different abilities and

attributes. Similarly, conditioning on the number of firms, populations with more diverse

firm age and size distributions likely exhibit even greater heterogeneity in the

characteristics they desire. Firms often imprint on a set of operating routines and a

production technology when they begin (Baron, Burton and Hannan 1996); hence, those

13

founded at different times often operate with varying production and organizational

models, potentially drawing on divergent employee abilities and attributes. Likewise,

firm size typically correlates to both market position and the method of production,

meaning that firms of varying sizes also likely prefer different employees (cf. Greve,

1994; Fujikawa-Greve & Greve, 2000).

Though less prominent than the vertical sorting models described above, some

theoretical work in economics building on the so-called “Roy model” follows a similar

line of reasoning. Roy (1951) presented a model of an economy with two sectors, hunters

and fishers (for formalizations, see: Sattinger, 1975; Heckman and Sedlacek, 1985;

Heckman and Honore, 1990). Each type of work requires its own set of skills. Employees

choose the sector in which they work on the basis of comparative advantage – in other

words, they select the job in which they can expect to be most productive, and

consequently to earn the highest wages. As a result of this type of self-selection, the two-

sector economy yields higher average and lower variance in wages as long as the

different skills do not correlate perfectly. Elaborations of this model have revealed that

the basic result holds even if workers do not know their types and must search

sequentially for the right employer for their skills (MacDonald, 1982). Empirical

verification of this model, however, has been limited to demonstrating that two- and

three-sector models of the economy explain the distribution of wages better than a one-

sector model (Heckman and Sedlacek, 1985; Gould, 2002). The Roy model, therefore,

while pointing to a similar logic for the link between organizational diversity and income

inequality, has only considered much coarser-grained differences across employers.

14

Vertical and horizontal sorting

Both perspectives we have described rely on a matching process between

employers and employees, but differ on a key assumption. Whereas the first set of

models, such as those proposed by Rosen (1981, 1982) and Wheeler (2000), assumes a

one-dimensional distribution of worker characteristics and employer interests, the

ecological perspective assumes that these distributions exist in a multi-dimensional space.

This subtle difference in assumptions, far from being simply an issue of theoretical

convenience, is the source of their opposing predictions regarding the effects of increases

in the number of firms in a labor market. The difference parallels the distinction between

vertical and horizontal differentiation in product markets in the marketing literature (cf.

Gabszewicz and Thisse, 1979; Shaked and Sutton, 1982). Under vertical differentiation,

one assumes that all buyers would prefer the same products (workers) at a fixed level of

price (e.g., virtually everyone would prefer a business class air ticket to coach if it did not

cost extra). Horizontal differentiation, on the other hand, allows for the possibility that

consumers (employers) prefer different product (employee) attributes.

We have little reason to believe, however, that the empirical reality of corporate

demography and labor markets corresponds neatly to either of these stylized assumptions;

changes in industrial demography can generate sorting along both the vertical and

horizontal dimensions. Individuals have qualitatively different abilities and attributes,

such that their desirability depends on the employer. If organizations differ sufficiently in

their needs, the competition for labor therefore may not generate the determinate rank

ordering envisioned in the vertical sorting model. Similarly, while individual

organizations may in principle occupy distinct niches, many organizations overlap highly

with each other in terms of their demand for labor (Sørensen, 1999, 2004), suggesting

15

that the impact of an increase in the number of firms depends on their diversity. Thus, it

does not seem inconsistent with the ecological argument to expect that increases in the

number of firms of a particular type could produce sorting and increased inequality.

In this sense, one can view the vertical sorting and ecological (or horizontal

sorting) arguments as complements to each other. Among organizations drawing on a

specific set of human resources, such as those operating within the same industry using

similar production technologies and hiring logics, the vertical sorting argument likely has

the greatest force in explaining the effects of increases in competition. By pointing to the

importance of vertical differentiation within a niche, it provides a richer

conceptualization of the ecological argument of the labor market consequences of

changes in industrial demography. The ecological insights, by contrast, highlight an

important role for organizational diversity neglected in the vertical sorting model’s

(implicit) assumption of horizontally undifferentiated firms. As firms within a labor

market draw on a wider range of human resources, vertical sorting – and with it wage

inequality – declines as employees more likely find firms that fit well to their abilities

and attributes.

EMPIRICAL STRATEGY

Our argument suggests that two dimensions of corporate demography contribute

importantly to the generation of inequality: the number and the diversity of employers.

We examined the impact of these factors using a unique dataset characterizing the Danish

labor market from 1980 to 1998. This dataset allows us to relate regional variation in

wage inequality among employed workers to regional differences in corporate

demography. We begin by simply comparing the gross income inequality in an industry

16

within a particular region to the distribution of firms in the region, both within and

outside the focal industry. This analysis offers a picture of the overall relationship

between corporate demography and wage dispersion. This gross relationship may result

from differences both in the demand for observable and unobservable individual

characteristics, as well as from endogenous processes influencing these distributions.

Some employers, for example, might prefer more experienced workers, while others

might desire greater levels of education. On the other hand, this analysis cannot account

for differences in inequality arising from exogenous differences in the characteristics of

workers – in other words, variation across regions in wage dispersion might reflect

heterogeneity in the distribution of employees rather than of employers. For example,

highly educated workers may concentrate in particular regions of the country. Hence, we

also considered a substantially more conservative approach, where we estimated the

degree of wage inequality, net of individual observable characteristics, to assess the

effects of corporate demography on income inequality.

Wage setting in Denmark

One would only expect the predictions of the two theories we have outlined to

hold in labor markets that meet certain scope conditions. Two conditions are particularly

important. First, since the matching of employees to employers likely occurs primarily

through the movement of employees between jobs and firms – at least within regions –

both theories presuppose that a fair degree of flexibility characterizes the labor market, in

the sense that both workers and firms can terminate employment relationships on short

notice. Second, for wages to reflect the quality of the match between the worker and the

firm, employers must also have some discretion over the wages that they pay to

17

individual workers so that they have the freedom to adjust pay to (perceived)

productivity.6

With respect to the first scope condition, observers generally consider the Danish

labor market quite flexible, particularly by European standards. Employers in Denmark

incur very low firing costs, leading it to have the lowest level of employment protection

among European OECD countries (OECD, 1994), at a level on par with the United States

(Bingley and Westergaard-Nielsen, 2003). Perhaps as a result, the Danish labor market

has both high rates of mobility between firms and relatively short lengths of firm tenure.

Albæk and Sørensen (1998), for example, estimated an average annual rate of job

creation of 12% and an average annual level of job destruction of 11.5%, between 1980

and 1991. By comparison, Davis and Haltiwanger (1992) estimated annual job creation

and destruction rates in U.S. manufacturing between 1980 and 1988 of 8.4% and 11%.

Furthermore, Denmark has a low mean firm tenure, at the bottom of the range for OECD

countries along with the United States, Australia and the United Kingdom (OECD, 1997).

Bingley and Westergaard-Nielsen (2003) argue that this fact both reflects the low degree

of employment protection and results from the high degree of wage compression within

firms, which encourages productive workers seeking pay increases to seek out higher-

paying employers.7

As for the second condition, wage setting in Denmark historically has been quite

centralized, thanks in part to the high rates of unionization (over 70% [Iversen, 1996]).

From the 1930s through the 1970s, centralized bargaining between associations with

6 In principle, the scope conditions of the theories could be met even if individual employers had to pay all employees performing the same task the same wage, regardless of individual differences in productivity – as long as heterogeneity existed among firms in the wage paid and the labor market allowed a sorting of workers to firms.

7 High rates of turnover also lower the value of firm-specific training, and therefore may cause employers to focus more strongly on employees whose skills match well to the job.

18

broad memberships representing organized labor on the one side and employers on the

other primarily determined wage rates, leading to extremely low levels of income

inequality relative to other countries (Iversen, 1996). During the period we study,

however, the centralized wage bargaining system began to break down. The first element

of this decentralization, during the early 1980s, involved a shift in the role of the

nationwide labor and employer associations from reaching enforceable agreements to

setting non-enforceable targets, allowing industry-level associations to negotiate

enforceable agreements (Iversen, 1996; Madsen, Andersen and Due, 2001).

Even greater employer discretion over wage setting came later in the 1980s as this

centralized system gave way to the so-called “normalløn” system. Under this regime,

employers could pay wage supplements to all employees in the firm, supplements to all

occupants of particular jobs, and performance bonuses, though these supplements still

required agreements between the firms and unions at the local level. Iversen (1996)

argues that much of the pressure for decentralization came from employers, who, in the

face of increased international competition, felt the need for greater control over their

incentive structures. Another important shift in the level of the centralization came in

1991 with the replacement of the nomalløn system with the “minimalløn” system.

Whereas the prior system primarily allowed for differentiation through bonuses or

distinct job titles, the minimalløn system relaxed restrictions on the normal wage rates

(without bonuses) for particular jobs. The centralized bargaining process largely limited

itself to setting a minimum wage for a job. Employers could then set the wage for a

particular worker according to the worker’s productivity, experience and effort.

19

The minimalløn system has spread rapidly in the Danish labor force. By 1997 (the

end of the period we study), wage systems that included decentralized wage setting

covered 84% of the private sector labor force (Dansk Arbejdsgiverforening, 2000). Thus,

although individual firms in the 1960s and 1970s played a relatively small role in setting

individual wage rates, their influence has increased dramatically in the 1980s and

particularly in the 1990s. Consistent with this increased decentralization of wage setting,

Bingley and Westergaard-Nielsen (2003) observe an increase in the returns to firm

tenure, which they interpret as evidence of the increased ability of firms to use incentives

to retain valuable workers.

Data and measures

We analyzed data from government registers maintained by Statistics Denmark

and collected in the Integrated Database for Labor Market Research. Referred to by its

Danish acronym, IDA, this database contains comprehensive, annual information on

individuals and work establishments in the Danish market. The data amount to an annual

census: IDA includes all individuals legally residing in Denmark in a given year.

Moreover, IDA contains a wealth of individual characteristics, including information on

family structure, educational attainment, income, and work experience. Most importantly

for our purposes, the dataset links individual employees to their work establishments and

employers. Though IDA contains only limited information about each of these

establishments, it does identify both their industry and geographic location. It categorizes

workplaces into one of 111 industries using a standard (ISIC, rev. 2) classification

scheme. Our analysis, however, did not extend to all of these industries. Notably, we

excluded industries in the primary (agricultural and extractive) sector, as well as

20

industries in which public sector employment accounted for more than 15% of the

workforce.8 As a result, the sample analyzed includes 81 industries.

With respect to geography, the database associates each workplace with a

township (“kommune” in Danish). Townships, the smallest administrative units in

Denmark, divide the country into 275 mutually exclusive and exhaustive regions. In

considering the analysis of regional variation in wage inequality, the appropriate level of

aggregation is a salient concern. In particular, the sorting and diversity arguments appear

potentially sensitive to the level of aggregation at which one computes the corporate

demography measures. For example, the presence of alternative industries in nearby

townships may affect workers in a township with limited industrial diversity. We see no

easy solution. Some scholars argue that “journey-to-work” boundaries should define

regional labor markets (Beggs and Villemez, 2001), but such boundaries become at least

partially endogenous to the attractiveness of the employment opportunities in a given

area. To assess the potential impact of measuring corporate demography at the lower

level of aggregation, we computed an alternative set of demographic measures using a

79-category aggregation of townships. This aggregation combines townships based on

commuting patterns in 1980 (Andersen, 2000), and thus corresponds to the definition of a

regional labor market in terms of journey-to-work boundaries. These alternative analyses

proved reassuring, as they paralleled the conclusions reached with the more

disaggregated measures that we report here.9

8 The distribution of public sector employment is highly skewed: 62 of the 111 industries have no

public sector employment, and in 87 industries (including the primary sector), less than 5% of employees work in the public sector.

9 We also estimated models that included dummy variables for the 16 counties in Denmark (the administrative units above townships), to account for potential spatial autocorrelation in the determinants of wage dispersion. McCall (2000) similarly uses state-level dummies to test for unobserved heterogeneity

21

Our analyses drew on a subset of the IDA database constructed and maintained by

the Center for Labor Market and Social Research in Denmark. This “Pay and

Performance” dataset covers all private-sector employees in a given year; it excludes

employees of the (sizable) public sector, the self-employed, and individuals not in the

labor force. For the purposes of our investigation, these exclusions make sense: the wage-

setting dynamics in the public sector likely depend on a host of factors not considered in

the theories outlined above, and the other two groups do not receive wages.

We analyzed data from 1980 to 1998. When estimating the models, we split the

analyses into two time periods: one running from 1980 to 1991, the other from 1992 to

1998. Two factors lead us to split the data along these lines. On the theoretical side, the

collective bargaining agreements reached in 1991 marked the earliest adoptions of the

minimalløn system for wages paid in subsequent years. As noted above, this system

substantially increased the level of flexibility available to employers in the wage setting

process, so we expected that the sorting processes might operate more strongly under this

system. From a more practical perspective, Statistics Denmark also shifted to a new

industry classification scheme in 1992. Though a mapping of old to new categories

exists, splitting the analysis offered a conservative approach to ensuring that this change

in coding would not influence our results.

To assess the influence of corporate demography on wage inequality, we

regressed two measures of wage dispersion on measures of the local industry

demography: gross wage dispersion and within-group wage dispersion.

across cities in the United States. Though the incorporation of these effects increases the standard errors, the results reported below remained robust to their inclusion.

22

Gross wage dispersion: We measured gross wage dispersion as the logged

standard deviation of wages across all workers employed within a particular industry

within a township.10 The models of gross wage dispersion included the mean wage for

workers in an industry in a township since the magnitude of the standard deviation

depends in part on the mean.

As noted above, this gross measures captures inequality from several sources: (i)

differential returns to observed characteristics across regions; (ii) differential returns to

unobserved characteristics across regions; (iii) endogenous investments in abilities and

attributes in response to these differential returns; and (iv) exogenous variation in the

distribution of individual characteristics. Although one might reasonably attribute the

first three to sorting processes, the fourth source belongs in a separate category. Hence,

the estimates using gross wage dispersion measure provide an upper bound on the

importance of corporate demography to inequality. An ideal measure would eliminate the

last, exogenous source alone. Doing so, however, is impossible with the data at hand, so

instead we turned to an even more conservative approach (a lower bound): We estimated

the effects of sorting stemming only from the second source – differential returns to

unobserved characteristics – by using the within-group wage dispersion as a dependent

variable.

Within-group wage dispersion: We estimated the effects of corporate demography

on within-group wage dispersion using a two-step hierarchical linear modeling strategy.

Our approach is similar to that adopted by McCall (2000) in her analysis of regional

10 Logging the standard deviation accounts for the likely distribution of the dependent variable.

The distribution of a sample of standard deviations from a lognormal distribution (which the raw wage data match almost perfectly) is log-normally distributed. Despite this fact, a set of models using the raw standard deviation as the dependent variable yielded substantively similar results.

23

wage inequality in the United States (see also Blau and Kahn, 1996; Rauch, 1993).11 In

the first stage we estimated, for each year, a linear regression model (using OLS) of an

employee’s log wage from their primary job as a function of a variety of individual

characteristics: occupation,12 labor force experience, labor force experience squared,

years of education, firm tenure, sex, marital status, an interaction between sex and marital

status, and the number of children under the age of two.13 These regressions also included

fixed effects for each industry and township. These fixed effects purged from the model

the mean wage in each industry as well as the mean wage in each township, ensuring that

the remaining variation in incomes does not reflect differences in levels across industries

and townships.

We used the first stage regressions to generate the measure of within-group

income inequality used in the second stage. The dependent variable for the second stage

is the natural log of the standard deviation of the residuals for workers in a particular

industry in a particular township.14 As McCall (2000: 419) notes, one can interpret the

residual standard deviation as “a measure of variation in the earnings of workers with the

same observed characteristics, some unknown portion of which is due to differences in

the distribution of, and returns to, unobserved characteristics.” We computed this

measure for each observed combination of industry i, and township j, at year t. The

11 Our estimation procedure differed from McCall’s (2000) in one respect. Where she estimated

separate regressions in the first stage for each region in her dataset, we estimated a pooled regression across all regions in the first stage. Since we split the sample into much smaller regions, separate regressions would in many cases entail very small sample sizes. Substantively, this difference implies that we assume that the income returns to the observable individual level characteristics (such as work experience) do not vary across regions.

12 Occupation here refers to seven broad categories ranging from top management to unskilled worker, entered as dummy variables.

13 Since the sample consists of all private sector employees with valid data in a given year, the sample sizes for the first stage regressions range from over 1.3 million to more than 1.6 million cases.

14 We adjust for sampling error by adding 1/(2*n) where n denotes the number of individuals in the cell (Bryk and Raudenbush, 1992).

24

logged residual standard deviation for cell i,j,t therefore becomes our measure of income

inequality among workers in industry i, and township j, for year t. Higher values indicate

greater dispersion in the incomes of these workers, net of their observed characteristics.

Measuring corporate demography: We generated three measures to assess the

salience of the demographic characteristics of the local industry population on wage

dispersion. First, we used the simplest representation of the population, the count of the

number of firms in an industry, to capture the level of within-industry labor market

competition. We experimented with different functional forms for the effect of the

number of firms. A comparison of the curve implied by the logged number of firms to a

seven piece spline revealed almost no difference between the two. In fact, the splined

estimation improved the variance explained by only 0.3%. Given this small difference,

we retained the more parsimonious models using the logged firm count. Second, since

markets with only a single employer in an industry may differ qualitatively from those

with two or more competing firms, we also included a dummy variable for those

industry-township cells with only one firm. Finally, using employment shares, we

calculated the standard deviation of firm size in the industry; to the extent that production

systems and/or hiring practices differ systematically with scale, this measure should also

capture horizontal sorting.

To measure the importance of the diversity of firm types in a local labor market,

we created two alternative measures. The number of industries simply counts the number

of industries represented in the local population of firms.15 This number does not,

however, account for the distribution of activity across these sectors, which also likely

15 Up to 111 industries may be present in any given township, since we include primary sector

industries and industries dominated by the public sector in this measure.

25

affects the diversity of opportunities available to any particular individual. Hence, we

calculated an entropy measure to capture both the number of industries represented in the

local population as well as the concentration of employment shares across them.16

In addition to these measures of interest, the models include measures of three

other characteristics of the local labor market: the total number of employees in the

township across all industries, the total number of employees in the township in the focal

industry, and the total number of employers in the township across all industries (see

Table 1 for descriptive statistics). To the extent that industries have common demands for

employee skills, one would expect wage inequality to rise with the total number of

employers in a township as a result of vertical sorting. Also, wage dispersion likely has a

negative relationship with both the total number of employees in a township and the

number of employees within a particular industry in a township. When controlling for the

number of employers, these measures essentially capture average organization size. If

wages vary less within than across organizations, one might therefore expect regions with

larger organizations to exhibit lower inequality.17

RESULTS

Table 2 reports OLS estimates of models of the effects of corporate demography

on gross income inequality for the period 1980 to 1991, along with standard errors

adjusted for the clustering of observations at the township level. Table 3 presents the

same models estimated for data from 1992 to 1998. All models included dummy

16 The entropy measure we use is -Σpilog(pi), where pi is industry i’s share of private employment

in a township. 17 Wages might vary less within organizations for a variety of reasons: Job classifications may

vary less within than across firms. Similarly wage-setting regimes typically differ more greatly across firms. Organizations may also compress wages in the interest of improving worker perceptions of fairness.

26

variables for year and industry, so the estimates reflect the impact of regional differences

in corporate demography on regional wage inequality after purging the data of common

industry and temporal components. The dependent variable in Tables 2 and 3 is the

logged standard deviation of wages, multiplied by 1,000 for ease of presentation.

The estimates in these two tables generally support the expectations derived from

the sorting processes. Consistent with the expectations of the vertical sorting argument,

the estimates in the first column of both Tables 2 and 3 indicate that the dispersion of

wages in an industry increases with the number of employers in that industry in a

township. The dummy variable for a single employer, moreover, reveals a pronounced

increase in inequality as a township moves from having one to two employers within a

particular industry. Total industry employment meanwhile tends to depress wage

dispersion. As noted above, when included in a model with the number of firms, this

variable provides information on average firm size. In essence, it suggests an inverse

correlation between wage inequality and average firm size, which one might expect if

wages vary less within than across firms.

The second models in Tables 2 and 3 introduced one measure of the diversity of

employment opportunities, the count of industries in the township. Consistent with the

expectations of the ecological diversity argument, this variable has negative coefficient

estimates in both time periods, although the effect is not statistically significant in the

second period (Table 3). The estimated effects of the alternative entropy-based measure,

included in the third column of the tables, also have the expected valence, but do not

prove statistically significant in either time period. The final two models in both Table 2

and Table 3, however, which include interaction effects between the diversity measures

27

and the logged number of employers, provide support for the ecological argument. In

both time periods, the level of local wage inequality in an industry declines as the

diversity of employers increases. Moreover, the statistically significant interaction effect

suggests that the benefits of organizational diversity increase as the pressure for vertical

sorting, driven by the number of employers in an industry, rises.

Although the results in Tables 2 and 3 provide evidence of the important role that

industrial demography plays in inequality, they cannot escape the criticism that the

distribution of workers with different human capital characteristics across regions may

not vary randomly with respect to the distribution of firms and industries. For this reason,

Tables 4 and 5 present estimates of the same models, except that we used our within

group (i.e. residual) measure of wage inequality, purged of observed human capital

characteristics (once again, multiplied by 1,000 for ease of presentation). The results

parallel those using the gross inequality measure as the dependent variable. Competition

among employers within an industry continues to have a substantial positive effect on

residual wage inequality. As before, the diversity of employers generally lowers wage

inequality, and the magnitude of the diversity benefit increases with the number of

employers in an industry (the interaction term).

In Tables 4 and 5, we also note that wage dispersion appears to decline with the

diversity of employer firm sizes. One could interpret this effect of employment

concentration in at least two ways. On the one hand, a large number of small firms may

generate more intense labor market competition (Guadalupe, 2003), thereby magnifying

the sorting effects and wage dispersion. On the other hand, diversity in firm size may

reflect differences in organizational models and production processes, and concomitantly

28

the degree of diversity in the opportunity structure (Hannan, 1988; Greve, 1994). Small

firms more likely engage in craft-like production, while larger firms tend toward more

automated, mass market models. Small firms also typically employ more informal hiring

procedures, which may favor different individuals from the more bureaucratic human

resource policies typical of larger firms.

DISCUSSION

Our statistical analyses of regional variations in wage dispersion in Denmark

indicate that the degree of inequality in a local labor market depends on the demography

of employers in that labor market. In particular, our analyses suggest that the dispersion

in wages among workers in an industry depends both on the number of co-located

employers in the same industry, and on the availability of employers with different

production processes and technologies. More pronounced competition within the industry

engenders greater inequality through vertical sorting, while increased organizational

diversity dampens it.

Though both vertical sorting and ecological diversity have significant effects, a

comparison of the relative magnitudes of these forces proves instructive. The

standardized coefficient estimates, reported in Table 6, point to a substantial vertical

sorting effect. For example, columns one through four indicate that a one standard-

deviation increase in the (log) number of firms leads to a 16%-19% increase in gross

inequality in both time periods. As noted earlier, however, this overall effect could stem

from multiple sources: differences in the matching process on both (i) observable and (ii)

unobservable characteristics between employees and employers; (iii) endogenous

heterogeneity across regions in human capital as a result of differences in the returns to

29

investments in education and experience; and (iv) exogenous variation in human capital

across regions.

The more conservative approach, reported in columns five through eight, focuses

only on the matching of employees to employers based on unobserved employee

attributes. Not surprisingly, this approach dramatically reduces the standardized effect. A

one standard deviation increase in the log number of firms in an industry only increases

the within group inequality by 5%-6%. The true total effect of vertical sorting on wages

falls somewhere between these two estimates. Though any estimate of total effects would

ideally exclude exogenous sources of productivity differences, they should include not

just the sorting on unobservable dimensions captured in the analysis of the residual wage

dependent variable, but also sorting on observable characteristics and endogenous

heterogeneity in human capital investment due to differences in employment

opportunities. Isolating the exact magnitude of the overall effect, however, will likely

prove elusive, as it requires a means of differentiating between exogenous differences in

the distribution of individual characteristics and endogenous investments in human

capital.18

By contrast, the magnitude of the diversity effects appears substantially smaller

than that of vertical sorting. The size of the diversity benefit for employees in a particular

industry, however, also depends on the number of firms in that industry, making

interpretation somewhat difficult. Consider the effects of the number of industries for

overall inequality in the first time period (the fourth model in Table 2); Figure 1

illustrates the effects graphically. Industrial diversity has little effect of its own on gross

18 The usual instrumental variables approaches to estimation do not apply in a straightforward

manner here because they depend on the relationship between the levels of variables rather than in the degree of variance produced by the sorting process.

30

inequality. It primarily acts to mitigate the intensity of vertical sorting. For example, at

the minimum level of industry diversity (a region with only one industry), a one standard

deviation increase in the number of firms in the industry corresponds to an 18% rise in

inequality. In a region with maximal diversity (including employers from all industries),

the same increase in the number of firms would result in only a 3% rise in gross wage

inequality.

Although the interaction effects make it difficult to parse the exact proportions,

our results suggest that, as measured here, vertical sorting processes account for more of

the variation in regional wage inequality than organizational diversity. At least two

factors could account for this imbalance. On the one hand, the relative importance of

vertical sorting may indicate that employers in different industries overlap to a large

extent in their labor requirements. In the vertical sorting argument, greater inequality

results as increased competition between firms magnifies individual differences in

productivity. A portion of these productivity differences stems from the fact that certain

individuals possess the specialized skills that some employers demand, while others do

not, as in our earlier example of baseball and basketball players. Yet these productivity

differences also stem from heterogeneity in general abilities and skills, transferable across

employers; the star basketball player will likely play baseball better than most other

people. The relative magnitudes of the vertical and horizontal differentiation effects

therefore depend on the extent to which employers overlap in their demands for labor; in

particular, as employers’ labor demands increasingly overlap, vertical sorting pressures

rise (cf. Gould, 2002).

31

On the other hand, this difference in the relative importance of vertical sorting

may reflect how well our measures of organizational diversity capture the extent of

horizontal differentiation among employers in their labor demands. Our measures of

diversity rely on the relatively coarse information available in an aggregated industry

classification, which renders at best a crude approximation of the true degree of

organizational diversity. Moreover, industry classification schemes have been developed

as a means of sorting organizations according to their output (products or services) and

may have limited power to distinguish across organizations in their demand for labor as

an input. Though imperfect, these industry codes nonetheless offer one of the few

accepted means for measuring organizational diversity on a large scale.

Although our estimation strategy only uses geographic variation as a means of

gaining empirical leverage on the identification of the effects of corporate demography

on inequality, our results nonetheless have interesting implications with respect to the

literature on economic geography. Industrial clusters typically refer to regions with a

large number of small firms operating in a single industry, where those firms account for

a large share of overall employment. Policymakers have shown considerable interest in

using industrial clusters as a model for economic development, and economists have

forwarded several economic models to explain why such a configuration of productive

activity might stimulate growth (for a review, see Sorenson and Audia, 2000). Little

attention, however, has been given to the potential consequences of clustering beyond

firm performance. Our results suggest that clustering may have important consequences

for the level of inequality in society. Clusters reside at the back, left corner of Figure 1

32

(many firms in a region with little industrial diversity); these regions generate the most

intense vertical sorting processes, and hence the greatest degree of income inequality.

The insight that corporate demography influences the stratification process

through its implications for the matching of individuals to employers also potentially

opens new ground for future research. For example, our current analyses do not consider

under what conditions these processes should operate most strongly. Future work may

thus consider what factors amplify and mitigate the effects of competition and sorting.

Consider, for example, search costs. These costs introduce friction into the matching

process, thereby reducing the efficiency of matches between firms and employees (i.e.

increasing the likelihood that a high quality firm employs a low quality employee) and –

because the inefficient matching leads to regression to the mean in firm productivity –

concomitantly depressing income inequality. Such search costs would have only limited

bearing on the relationship between organizations and inequality if all firms encountered

equivalent costs, but they may vary systematically across firms or industries due to labor

demands or operating routines (e.g., Gould, 2002), or across regions as a result of

differences in institutional environments (McCall, 2000).

Individuals may also vary in the degree to which these sorting processes constrain

them. The persistence of differences across regions in their local inequality depends to

some extent on the geographic immobility of individuals; otherwise, the entire country

would operate as a single labor market and regions would differ little in their degrees of

wage dispersion. Individuals nonetheless differ in the degree to which they remain rooted

in a local community. For instance, women, and particularly single mothers, typically

commute much shorter distances than men (e.g., Gordon, Kumar and Richardson, 1989).

33

If men’s greater proclivity to travel to work allows them access to regions offering higher

returns for their skills, this difference in geographic mobility could contribute to

inequality between men and women in labor market outcomes. Hence, future research

might fruitfully investigate the ways in which organizational demography contributes to

stratification across different types of individual attributes.

CONCLUSION

Few sociologists today would deny the important ways in which organizations

“link the ‘macro’ and ‘micro’ dimensions of work organization and inequality” (Baron

and Bielby, 1980: 738). Indeed, decompositions of the sources of income inequality

across individuals suggest that cross-firm differences in compensation account for as

much inequality as human capital measures (Groshen, 1991), and that the importance of

these factors in explaining inequality may have risen over the last three decades

(DiNardo, Fortin and Lemieux, 1996). At the same time, a curious disjuncture has

developed in the literature, where work on the role of organizations in the stratification

process has largely grown apart from a larger literature on the determinants of inequality

at higher levels of analysis, such at the regional level (e.g., McCall, 2000) or across

society as a whole (e.g., Nielsen and Alderson, 1997), which scarcely mentions the

importance of organizations in this process.

This state of affairs reflects the fact that research on the role of organizations in

stratification has largely adopted a “focal organization” perspective (Scott, 2002) and

thus typically does not consider how these organizational level outcomes aggregate to

produce inequality at the societal level. The simple summation of processes internal to

individual, focal organizations offers one means of aggregating these outcomes to more

34

macro levels of inequality. But such an approach could easily lead researchers astray.

Individual organizations reside within a broader ecology of organizations, and

competitive (as well as symbiotic) relationships between firms have important

implications for organizational behavior.

Though beyond the scope of our research, our results may contribute to a better

understanding of the broader trends in income inequality. For instance, one of the puzzles

in inequality research concerns the remarkable rise in wage and income inequality in

advanced economies, particularly in the last decades of the twentieth century, following

decades of decline in inequality (Nielsen and Alderson, 1997; Morris and Western,

1999). Though a wide variety of factors likely contribute to this upswing in inequality,

one commonly discussed factor is the change in the industrial structure of advanced

economies (Morris and Western, 1999). This change in structure has largely taken the

form of a reduction in industrial diversity, as employment has moved away from a

declining manufacturing sector to service sector industries. To the extent that different

sectors increasingly relying on the same types of skills, increased inequality emerges as a

consequence of this process (cf. Gould, 2002). Changes in the number and size

distribution of firms over time may also contribute to rising inequality. In the first half of

the century, the number of employers declined rapidly as industries consolidated to

realize economies of scale through mass production. More recently, however, more

flexible manufacturing technologies have engendered a boom of specialists, dramatically

expanding the number of employers in many industries and reducing average firm size

(Carroll and Hannan 2000: 20). The coincidence between these trends suggests that

35

future research might also usefully consider the linkage between the evolution of industry

structure and societal levels of inequality.

36

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Table 1: Descriptive Statistics 1980-1991 1992-1998 Variable Mean σ Mean σ

Wage inequality 3.628 0.705 3.975 0.628

Log mean industry wage 4.470 0.351 4.874 0.267

Residual wage inequality -1.074 0.413 -1.128 0.411

Industry employment in township 112.417 350.516 110.093 316.143

Total township employment (000) 7.612 20.096 8.070 19.677

Total N firms in township 747.744 1511.421 716.193 1392.012

Single industry employer 0.089 0.285 0.109 0.311

Standard dev. of employer sizes 13.857 54.975 14.295 58.355

Log N industry firms in township 1.718 1.015 1.627 1.023

N industries in township 51.866 19.422 56.142 20.411

Entropy of industry shares 3.232 0.519 3.307 0.522

Note: Wage inequality is the log standard deviation of wages in an industry-township cell. Residual wage inequality is the log standard deviation of the residuals from the first stage human capital equation. See text for details.

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Table 2: Fixed effects estimates of the effects of corporate demography on wage inequality, 1980-1991

Variable (1) (2) (3) (4) (5) Log Mean industry wage 1,910.976† 1,913.112† 1,911.863† 1,911.791† 1,910.232† (15.401) (15.484) (15.430) (15.392) (15.282) Industry employment in township -0.041* -0.044* -0.042* -0.028 -0.040* (0.017) (0.018) (0.018) (0.017) (0.018) Total township employment (000) -3.207† -3.746† -3.783† -4.285† -4.875† (0.860) (0.810) (0.947) (0.733) (0.897) Total N firms in township 0.041† 0.050† 0.050† 0.067† 0.070† (0.012) (0.011) (0.013) (0.010) (0.012) Single industry employer -156.029† -153.331† -155.219† -124.276† -135.810† (11.823) (11.843) (11.908) (10.526) (11.170) Standard dev. of employer sizes -0.067 -0.055 -0.067 -0.108 -0.078 (0.059) (0.058) (0.059) (0.065) (0.063) Log N industry firms in township 150.102† 156.239† 152.367† 169.126† 160.128† (6.019) (6.244) (6.256) (4.802) (5.527) N industries in township -0.496* -0.990† (0.218) (0.211) Entropy of industry shares -8.926 -21.318† (6.624) (6.511) Log N firms * N industries -1.227† (0.151) Log N firms * Entropy -34.043† (6.001)

Note: The dependent variable is the log of the standard deviation of hourly wages for employees in a given industry in a township, multiplied by 1,000. Standard errors are adjusted for clustering at the township level. Models include dummy variables for year and industry. Interaction effects are centered. N for all models is 108,537 industry-township cells. Two-sided t-tests: * p<.05 † p<.01

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Table 3: Fixed effects estimates of the effects of corporate demography on wage inequality, 1992-1998

Variable (1) (2) (3) (4) (5) Log Mean industry wage 1,724.802† 1,725.637† 1,725.509† 1,721.599† 1,722.756† (16.868) (16.928) (16.896) (16.913) (16.918) Industry employment in township -0.077† -0.078† -0.078† -0.056* -0.076† (0.028) (0.028) (0.029) (0.027) (0.029) Total township employment (000) -2.143 -2.355* -2.685* -2.431* -3.438* (1.191) (1.200) (1.357) (1.211) (1.421) Total N firms in township 0.029 0.032 0.037 0.043* 0.052* (0.017) (0.017) (0.019) (0.018) (0.021) Single industry employer -148.942† -147.866† -148.172† -125.764† -134.023† (13.034) (13.110) (13.138) (12.631) (13.278) Standard dev. of employer sizes 0.097 0.102 0.097 0.044 0.091 (0.055) (0.055) (0.055) (0.062) (0.058) Log N industry firms in township 136.905† 139.460† 139.164† 151.738† 146.147† (6.310) (6.675) (6.881) (5.628) (6.593) N industries in township -0.211 -0.721† (0.238) (0.226) Entropy of industry shares -8.650 -19.331* (7.858) (7.583) Log N firms * N industries -1.205† (0.149) Log N firms * Entropy -29.350† (7.374)

Note: The dependent variable is the log standard deviation of hourly wages for employees in a given industry in a township, multiplied by 1,000. Standard errors are adjusted for clustering at the township level. Models include dummy variables for year and industry. Interaction effects are centered. N for all models is 65,837 industry-township cells. Two-sided t-tests: * p<.05 † p<.01

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Table 4: Fixed effects estimates of the effects of corporate demography on residual wage inequality, 1980-1991 Variable (1) (2) (3) (4) (5) Industry employment in township -0.044 -0.048 -0.045 -0.039 -0.044 (0.026) (0.027) (0.026) (0.027) (0.027) Total township employment (000) 0.997 0.401 0.606 0.115 -0.155 (1.422) (1.432) (1.568) (1.411) (1.511) Total N firms in township -0.009 0.000 -0.004 0.009 0.010 (0.020) (0.020) (0.022) (0.020) (0.021) Single industry employer -168.704† -165.632† -168.146† -150.574† -154.826† (10.644) (10.679) (10.665) (10.135) (10.720) Standard dev. of employer sizes -0.384† -0.370† -0.384† -0.397† -0.392† (0.114) (0.112) (0.113) (0.120) (0.118) Log N industry firms in township 38.877† 46.004† 40.465† 52.664† 45.745† (5.565) (5.657) (5.872) (4.650) (5.354) N industries in township -0.565* -0.821† (0.220) (0.211) Entropy of industry shares -6.122 -14.655* (7.027) (6.949) Log N firms * N industries -0.635† (0.124) Log N firms * Entropy -23.356† (4.642)

Note: The dependent variable is the log standard deviation of the residuals from the first-stage human capital equation regressions adjusted for sampling error, multiplied by 1,000. See text for details. Standard errors are adjusted for clustering at the township level. Models include dummy variables for year and industry. Interaction effects are centered. N for all models is 108,658 industry-township cells. Two-sided t-tests: * p<.05 † p<.01

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Table 5: Fixed effects estimates of the effects of corporate demography on residual wage inequality, 1992-1998

Variable (1) (2) (3) (4) (5) Industry employment in township -0.051 -0.056 -0.052 -0.044 -0.050 (0.030) (0.031) (0.030) (0.031) (0.030) Total township employment (000) -0.549 -1.106 -1.162 -0.875 -1.503 (1.012) (0.980) (0.977) (1.139) (1.105) Total N firms in township 0.010 0.020 0.015 0.026 0.027 (0.015) (0.014) (0.017) (0.014) (0.016) Single industry employer -117.412† -114.534† -116.944† -102.409† -105.425† (11.682) (11.784) (11.719) (11.188) (11.516) Standard dev. of employer sizes -0.226* -0.213* -0.226* -0.244* -0.231* (0.094) (0.092) (0.094) (0.100) (0.099) Log N industry firms in township 42.425† 49.378† 43.817† 56.023† 49.402† (6.268) (6.655) (6.731) (5.739) (6.176) N industries in township -0.565† -0.847† (0.210) (0.200) Entropy of industry shares -5.241 -13.984* (7.030) (6.645) Log N firms * N industries -0.659† (0.124) Log N firms * Entropy -23.884† (5.153)

Note: The dependent variable is the log standard deviation of the residuals from the first-stage human capital equation regressions adjusted for sampling error, multiplied by 1,000. See text for details. Standard errors are adjusted for clustering at the township level. Models include dummy variables for year and industry. Interaction effects are centered. N for all models is 65,894 industry-township cells. Two-sided t-tests: * p<.05 † p<.01

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Table 6: Effects of one standard deviation increases in independent variables on gross and within group wage dispersion

Gross dispersion Within group dispersion 1980-1991 1992-1998 1980-1991 1992-1998 (1) (2) (3) (4) (5) (6) (7) (8)

Industry employment in township -0.01 -0.01 -0.02 -0.02 -0.01 -0.02 -0.01 -0.02

Total township employment -0.08 -0.09 -0.05 -0.07 -0.00 -0.00 -0.02 -0.03

Vertical sorting

Total N firms in township 0.11 0.11 0.06 0.08 0.01 0.02 0.04 0.04

Single industry employer‡ -0.12 -0.13 -0.13 -0.14 -0.14 -0.17 -0.11 -0.11

Log N industry firms in township 0.19 0.18 0.17 0.16 0.06 0.05 0.06 0.05

Horizontal sorting

SD of employer sizes (/ 10) -0.06 -0.04 0.02 0.05 -0.22 -0.21 -0.14 -0.14

N industries in township -0.02 -0.02 -0.02 -0.02

Entropy of industry shares -0.01 -0.01 -0.01 -0.01

Note: Cell entries are the standardized coefficient estimates for the respective standard dependent variables, computed from the relevant models in Tables 2-4. The effect of the single industry employer dummy variable is reported as a change from 0 to 1.

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Figure 1: Joint effects of the number of firms and industry diversity on gross wage inequality

5 15 25 35 45 55 65 75 85 95 1050

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