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Do Unions Affect Labor’s Share of Income:
Evidence Using Panel Dataajes_792 784..810
By RUDY FICHTENBAUM*,†
ABSTRACT. There have been a number of studies analyzing the impact
of unions on labor’s share of income. Most have relied on either time
series or cross-section data. The purpose of this paper is to determine
the impact of unions on labor’s share of income in the U.S. This study
adds to the understanding of this topic by developing an analytical
model of imperfect competition and estimating the model using panel
data for the manufacturing sector. This study finds that unions have a
positive impact on labor’s share of income. Specifically, this paper
finds that labor’s share declined 17.9 percent between 1997 and 2006
whereas, if unionization density had remained at its 1997 level, labor’s
share would have declined only 13.9 percent. Thus, the decline in
unionization explains about 29 percent of the decline in labor’s share
of income. This paper is important for three reasons. First, this paper
sheds light on whether social and institutional forces play an impor-
tant role in determining the distribution of income between labor and
capital. Second, it helps to explain recent increases in wage inequality.
Third, it has implications for understanding the potential impact of
legislation, such as the Employee Free Choice Act, that would make it
easier for workers in the U.S. to unionize.
Introduction
The impact of unions on the functional distribution of income has
been widely debated by economists. Orthodox economists generally
argue that rather than reducing profits, union wage gains come at the
expense of non-union workers (Pencavel 2005). In part, this position
*I would like to thank my colleague Jim Vance and two anonymous referees for a
number of helpful comments and suggestions on an earlier version of this paper. The
usual disclaimer applies.
†Department of Economics, Wright State University, 3640 Colonel Glenn Hwy.,
Dayton, OH 45424, 937-775-3085, rudy.fichtenbaum@wright.edu.
American Journal of Economics and Sociology, Vol. 70, No. 3 (July, 2011).
© 2011 American Journal of Economics and Sociology, Inc.
is based on the view that the economy is perfectly competitive in both
the product and labor markets. If markets are viewed as being
competitive, then social and institutional forces will not influence the
distribution between labor and capital. Post-Keynesians and other
heterodox economists have challenged this view, arguing that it is
entirely possible for wage gains to come at the expense of profits. This
perspective is based on viewing the economy as being imperfectly
competitive in both the product and labor markets (Kalecki 1971;
Erickson and Mitchell 2007). Thus, from a post-Keynesian and het-
erodox perspective, social and institutional factors are important deter-
minants of the distribution of income between labor and capital
(Kalecki 1971; Robinson and Eatwell 1973).
The mainstream economics perspective argues that social and eco-
nomic policy cannot be used to address growing concerns of rising
inequality. Rising inequality is largely attributed to skill-biased tech-
nological change, which is seen as an exogenous variable outside the
control of public policy. In contrast, heterodox economists argue that
rising inequality is the direct result of public policy changes. Many
have argued that American corporations have consciously opted for a
“low road” strategy eroding social safety nets, holding down minimum
wages, destroying unions, increasing the use of temporary workers,
and investing in finance while divesting from manufacturing (Harrison
and Bluestone 1988; Harrison 1994; Gordon 1996; Koeniger et al.
2007).
The purpose of this paper is to determine the impact of unions on
labor’s share of income in the U.S. manufacturing sector using 1997–
2006 panel data. This paper is important for three reasons. First, it
sheds light on whether social and institutional forces play an impor-
tant role in determining the distribution of income between labor and
capital. Second, it helps to explain recent increases in wage inequality.
Third, it has implications for understanding the potential impact of
legislation, such as the Employee Free Choice Act, that would make it
easier for workers in the U.S. to unionize.
The paper is organized as follows. The next section presents a
review of the literature. The third section examines the decline in
labor’s share of income in the U.S. manufacturing sector. The follow-
ing section presents a model of the factors that determine labor’s share
Do Unions Affect Labor’s Share of Income 785
of income based on the assumption that a firm maximizes profits in an
oligopolistic industry. The fifth section presents an empirical model,
discusses the data used in this paper, and presents the estimates of the
model. The final section presents a summary and conclusions.
Review of the Literature
The impact of labor unions on labor’s share of income has been the
subject of numerous studies. Early studies were mainly descriptive in
nature and relied on time series data. Summaries of early research can
be found in Kerr (1957), Dobb (1959), Simler (1961), and Rees (1962).
In this early literature, the general consensus was that unions did not
appear to have a significant effect on labor’s share of income. For the
most part, these early studies were descriptive and examined how
labor’s share of income changed over time and compared the changes
to the growth in unionization.
Some studies, for example, Johnson (1954), used aggregate time
series data. Johnson (1954)—who Rees (1962) cites as providing
evidence that unions did not appear to have an impact of labor’s share
of income—only mentions unions once in the article. Rees’ conclusion
was based on Johnson’s observation that union growth did not
coincide with the rise in labor’s share of income. Johnson’s primary
explanation for the rise in labor’s share was based on the relative
expansion of employment in trade and services where labor’s share of
income is high, and the corresponding decline in agricultural employ-
ment where labor’s share of income is low. Johnson’s data does not
support this conclusion because it is aggregate data; but he cites
studies by Kuznets (1941) and Denison (1952) in support of his view.
Others, for example, Simler (1961), used industry data in the
manufacturing sector and found that there was no significant corre-
lation between unionization and labor’s share of income. Even Dobb
(1959), who is certainly sympathetic to the view that unions should
raise labor’s share of income, remarked that labor’s share of income
showed remarkable stability, both in the short and long run, despite
the growth of trade unions.
Perhaps the one exception in these early studies was that of Kalecki
(1954). In his study of the distribution of national income, he notes a
786 The American Journal of Economics and Sociology
long upward trend in the relative share of wages in U.S. manufacturing
and attributes this change to a fall in the monopoly power and the
strengthening of unions after 1933.
Beginning in the 1950s and 1960s orthodox economists embraced
human capital theory, according to which anyone engaged in market
activity can be seen as making investment decisions; some invest in
human capital while others invest in physical capital. Given this
perspective, the functional distribution of income is a meaningless
category because all that matters is inequality in the ownership of the
factors of production among households. This leads orthodox econo-
mists to focus on the size of the distribution of income and
de-emphasize the functional distribution of income because all market
participants are viewed as investors
Despite the de-emphasis on the importance of the functional dis-
tribution of income there have been a number of studies in recent
years that rely on modern econometric techniques. These studies can
be divided into two major groups. The first group consists of studies
that directly examine the impact of unions on labor’s share of income.
The second group consists of a number of studies that address the
topic indirectly, looking at whether increases in wages affect the cost
of production or profits, and examining the relationship between
unions and the wage-productivity gap.
The studies that look at the direct impact of unions on labor’s share
of income can be divided into three categories or approaches: 1)
time-series studies, 2) inter-industry studies using cross-section data,
and 3) cross-country studies using panel data.
One of the first studies using modern econometric techniques with
time-series data was by Kalleberg et al. (1984). Using time series data,
they look at factors affecting labor’s share of income in the printing
industry. In defining labor’s share, they use both wages of production
workers and total employee compensation. They argue that the nar-
rower definition may more accurately reflect “the working class” but
at the same time the broader definition includes non-wage compen-
sation, which they acknowledge as growing in importance, particu-
larly for workers involved in collective bargaining. Their regression
holds constant economic conditions, employer power, and worker
power, and examines how these factors have affected labor’s share of
Do Unions Affect Labor’s Share of Income 787
income from 1946 to 1978. Using both narrow and broad definitions
of “labor’s share,” their results show that both union density and strike
frequency had a positive impact on labor’s share of income. However,
they also find that this effect diminishes over time. The most obvious
limitation of this study is that the results may not extend beyond the
printing industry.
A second time-series study by Fichtenbaum (2009) looked at the
impact of unions on labor’s share of income in U.S. manufacturing
from 1949–2006. This study relies on a model of imperfect competi-
tion, holding constant the capital-labor ratio, the ratio of non-
production to production workers, capacity utilization, and trade.
Using several definitions of labor’s income, ranging from narrow to
broad, it finds that unions have a positive impact on labor’s share of
income.
The second group of studies has looked at this issue from an
industrial organization perspective taking into account how factors
like industry concentration, advertising to sales ratios, capital intensity,
and unionization affect labor’s share of income using cross-section
data from the manufacturing sector. This group includes studies by
Cowling and Molho (1982), Conyon (1994), Hollander (1982), Drou-
copoulos and Lianos (1992), Brush and Crane (1984), Henley (1987),
and MacPherson (1990).
In the U.K., Cowling and Molho (1982) found only weak evidence
that unions have an impact on labor’s share. Their study covers the
years 1968 and 1973. For 1968, they use two measures of union
power—the work stoppage rate averaged over two years and union
membership in 1963. If changes in unionization across industries
between 1963 and 1968 were not proportionate, then the measure of
union power being used would produce biased estimates. For the
models using the 1973 data, three measures of union power were
used: the stoppage rate, days lost as proportion of employment, and
coverage of collective bargaining agreements. However, the 1973
models did not control for the advertising to sales ratio or imports, so,
again, the estimates on the variables representing union power may
have been biased.
Similarly, using data for the U.K., Conyon (1994) found that
unionization had a positive effect on the share of income received
788 The American Journal of Economics and Sociology
by production workers. However, he also found that this effect
disappears when one takes into account industry-specific effects. He
uses five measures of union power—coverage of male manual
workers in 1985, the proportion of male manual employees covered
by national and supplementary agreements in 1985, the proportion
of male manual employees covered only by national agreements in
1985, the proportion of male manual employees covered by supple-
mental agreements in 1985, and the proportion of all employees
whose pay and conditions are directly or indirectly covered by
major collective bargaining agreements from 1983–1986. One
obvious weakness in this study is that the pooled data is being used
with four out of the five measures of union power being only
available for the year 1985. In addition, the first four measures of
union power were only for males and unionization; while union-
ization rates were falling rapidly in the 1980s in the U.K., they were
falling faster for males than for females. Clearly, this could result in
biased estimates. While being more inclusive, Conyon’s last defini-
tion is based on unpublished data and it is difficult to evaluate how
robust the change in results is when moving from a pooled regres-
sion to a fixed effects regression.
Using cross-section data for manufacturing industries in Canada,
Hollander (1982) found a negative relationship between the “non-
wage share” of income and unionization. Thus, he concluded that
“unionization increases the share of value added going to labor.”
Droucopoulos and Lianos (1992) have also studied the impact of
unions on labor’s share in Greek manufacturing industries. Unlike
other studies in this group, they use the ratio of strikes of wage and
salaried employees in proportion to total employment as a measure
of union power. They also estimate separately the relevant param-
eters in their model for wage employees and salary employees.
Their results show that strike activity increases labor’s share for both
groups.
In the U.S., Brush and Crane (1984) find no support for a positive
relationship between unionization and labor’s share of income. Using
data from the U.S. Census of Manufactures at a four-digit SIC level,
they define labor’s share by multiplying the wages of production
workers by the ratio of total labor costs to payroll (in order to adjust
Do Unions Affect Labor’s Share of Income 789
for fringe benefits), and by subtracting advertising expenses from
value added. However, Henley (1986) has criticized their results,
pointing out that matching three-digit union data to four-digit industry
data results in measurement error, thus reducing the probability of
finding a positive relationship. Henley (1987) uses cross-section data
from the 1972 U.S. Census of Manufacturers at the three-digit SIC level
and finds strong evidence that unionization is positively associated
with labor’s share of income. Specifically, he measures labor’s share
by using wages of production workers, total payroll, and total com-
pensation. In particular, he finds that higher levels of unionization are
positively correlated to all three measures of labor’s share, with the
strongest relationship between unionization and labor’s share mea-
sured using production workers wages.
Finally, MacPherson (1990) adapts Henley’s aforementioned model
adding measures of worker characteristics and establishment size to
the model, and he tests the model using 72 U.S. manufacturing
industries using three-digit Census of Manufacturers data for 1973–
1975 and 1983–1985. MacPherson uses two definitions of labor’s
share. The first includes compensation for production workers, which
is estimated assuming that compensation for production workers is
proportionate to that of all employees. His second definition measures
labor’s share using total compensation for all employees. His analysis
finds a strong positive relationship between union density and labor’s
share of income.
The third group of studies uses cross-country panel data to analyze
the impact of unions on labor’s share income. Bentolila and Saint-Paul
(2003) study factors explaining the movement in labor’s share of
income using panel data for 13 industries in 12 OECD countries from
1972 to 1993. They measure labor’s share in the private business sector
and include imputed labor remuneration for self-employed workers.
They begin by showing that there is a relationship between labor’s
share and the capital output ratio, which they refer to as an SK
schedule. They also introduce several factors that might shift this SK
schedule, including total factor productivity, changes in employment,
the real price of oil, and a labor conflict rate. Controlling for all of
these factors, they find that there is no significant relationship between
labor conflict and labor’s share.
790 The American Journal of Economics and Sociology
Finally, Carter (2007) estimates a panel data model to explain labor’s
share by using data taken from the Extended Penn World Tables for
15 high-income countries from 1963 to 1996. Specifically, he estimates
a model where labor’s share is a function of the unemployment rate,
union density, and the capital-labor ratio. He finds that union density
has no significant impact on labor’s share of income. In part, this result
may be influenced by the fact that some countries have low union
density when measured using union membership but collective bar-
gaining agreements cover a significant number of workers.
Both Carter (2007) and Bentolila and Saint-Paul (2003) use overly
broad definitions of labor. Both define labor as anyone who receives
a wage or salary and Bentolila and Saint-Paul (2003) include imputed
remuneration for the self-employed. This definition includes catego-
ries of employees (such as managers) who would not even be eligible
to join a union. Thus, it is not particularly surprising that these studies
find that unions do not appear to have an impact on labor’s share of
income.
The second major group of studies looks indirectly at the effects of
unions on labor’s share of income. Within this group of indirect
studies, three approaches have been taken: 1) estimating the impact of
wage increases on the increase in total costs, 2) looking at the impact
of unions on the wage-productivity gap, and 3) examining the impact
of unions on profits. In the first type of studies, if unions raise wages
but those increases have no impact on total costs, then by implication
unions will have no effect on labor’s share of income. In the second
type of studies, if unions cause the gap between real wage growth and
productivity growth to expand, then by implication unions will raise
labor’s share of income. Finally, in the third category of studies, we
find that unions lower profits, and if capital’s share of income is lower,
then by implication labor’s share of income will be higher.
Ahlseen (1990) uses cross-section data for industries and states
from the 1958 U.S. Census of Manufacturers. Since there is no data
on the level of unionization that is broken down by state and by
industry, he approaches the question of union influence on labor’s
share indirectly by estimating translog cost share equations for
capital, non-production labor and production labor in seven two-
digit industries for 15 to 28 states. He finds that for three of the
Do Unions Affect Labor’s Share of Income 791
seven industries, the data does not satisfy the concavity assumption
needed to use a translog cost function. In the four industries that
provide consistent estimates of the cost share equations, the coef-
ficient that measures the elasticity of the cost of production workers
with respect to their wage rate is never statistically significant. Based
on these results, Ahlseen (1990) argues that unions may raise wages
for production workers but that the higher wages do not have an
impact on the cost share of income received by production workers.
Therefore, he concludes that unions do not have an impact on
labor’s share of income.
The second set of studies using the indirect approach explores the
impact of unions on the wage-productivity gap. If the real wage rate
increases at the same rate as labor productivity, then labor’s share will
remain constant. Since the late 1970s, the gap between the growth rate
of real wages and the growth of labor productivity has increased,
which is consistent with labor’s declining share of income. If the
increase in this gap is due in part to declining unionization, then there
will be a positive relationship between unionization and labor’s share
of income.
Ferguson (1996) finds that 18 percent of the growth in the wage-
productivity gap after 1981 is explained by a decline in employment
in unionized industries. Furthermore, he finds that another 25 percent
of the growth in the wage-productivity gap was explained by a decline
in the ability of unions to raise wages, a decline in union bargaining
power. However, in a study that focuses on the wage-productivity gap
in manufacturing industries, Zavodny (1999) finds that the gap had not
grown faster in industries with declining unionization, and therefore
concludes that declining unionization was not responsible for the
growing gap.
The last type of studies taking the indirect approach assesses the
impact of unionization on profits. Freeman and Medoff (1984) and
Voos and Mishel (1986) find that unions reduce profitability. While this
finding does not provide direct evidence that workers capture these
profitability losses, it is certainly consistent with studies showing that
unionization is positively related to labor’s share.
In summary, a number of studies have explored the relationship
between changes in unionization and changes in labor’s share of
792 The American Journal of Economics and Sociology
income. Specifically, we have examined direct studies using three
types of data: time-series, cross-section industry data, and cross-
country panel data. In addition, we examined a number of studies that
look at the impact of unions on labor’s share of income indirectly
estimating: the impact of changes in wages on total cost, the impact of
unions on the wage-productivity gap, and the impact of unions on
profits. However, as this review of the literature demonstrates, the
evidence is not conclusive one way or another. The remainder of this
paper explores the impact of unions on labor’s share of income in the
U.S. manufacturing sector by using panel data.
Labor’s Share of Income
To understand the potential impact of unions on the distribution of
income, it is important to define labor in such a way that identifies a
particular group of workers who are potentially affected by unioniza-
tion. Ideally, we would like to distinguish “managerial workers” who
are not eligible to join a union from non-managerial workers who
have the right to join a union.
Orthodox economists tend to view the economy as being perfectly
competitive and define labor as any human activity that takes place in
a market void of social relationships. Consequently, they view labor as
being any activity for which an individual receives a wage or salary,
thereby conflating different types of human activity. From their per-
spective, there is no difference between the work performed by a CEO
and that performed by a production worker in a factory: they are both
forms of “labor.”
In fact, orthodox economists have in effect eliminated labor alto-
gether, transforming it into human capital. By defining labor as
being synonymous with engaging in market activity that is rewarded
with the payment of wages or a salary, the growing inequality
between CEOs and workers will have no impact on labor’s share of
income.
In contrast with the perspective of orthodox economists, post-
Keynesians and other heterodox economists eschew the notion that
the economy is governed by perfect competition. Rather, they start
with the proposition that forms of imperfect competition dominate the
Do Unions Affect Labor’s Share of Income 793
economy. Moreover, they view economic relationships as fundamen-
tally social in nature, thus social class cannot be ignored.
Ideally, we would like to define labor in terms of social classes,
which are defined by historic forms of property relations and the
organizational structure of production (Zweig 2000). This would lead
us to define labor as consisting of non-managerial employees.
The principal sources of data to measure labor’s share of income in
U.S. manufacturing, both provided by the U.S. Census Bureau, are the
Annual Survey of Manufactures (ASM) and the Census of Manufactures
(CM). Unfortunately, data from the ASM and the CM do not distinguish
between managerial and non-managerial employees, but they make
a distinction between production and non-production employees
instead.
Therefore, we define labor’s share, in the U.S. manufacturing sector,
to mean the wages or wages and benefits received by production
workers as a proportion of value added in manufacturing. For the
most part, in the U.S. manufacturing sector, most unionized workers
are production workers. Thus, if unions do have an effect on labor’s
share of income, then this effect should be on the share of income
earned by production workers.
This definition of labor is not perfect because it excludes some
non-supervisory workers who are either unionized or have the poten-
tial to unionize. However, it does encompass the core of workers that
historically have unionized in the manufacturing sector. Since the
primary purpose of this paper is to understand the effects of unions on
labor’s share of income, this definition seems appropriate given the
limitations of existing data.
One of the primary goals of this paper is to use panel data to
examine the impact of unions on labor’s share of income in manu-
facturing. There are two possible ways of forming panel data. The first
would be to use industry data. Using industry data presents several
challenges. Perhaps the most important one is that industry data
would require estimates of union membership at a three- or four-digit
level. Union membership estimates come from the Current Population
Survey (CPS) and the sample size of the CPS is too small to make
union membership estimates at the three- or four-digit level on an
annual basis. Cross-section studies can use an average union mem-
794 The American Journal of Economics and Sociology
bership over a few years. However, using moving averages of union
membership with panel data would reduce cyclical variation in this
data. Therefore, the data used in this study will be panel data covering
the 50 U.S. states and the District of Columbia from 1997 to 2006. We
have chosen to start the panel in 1997 because that is the first year in
which the North American Industry Classification System (NAICS)
replaced the Standard Industrial Classification (SIC) system.
Figure 1 shows the trend in labor’s share of income (wages of
production workers as a proportion of value added) for manufacturing
in the U.S. from 1997 to 2006. Over the 1997–2006 period, labor’s
share of income declined by 3.6 percentage points. Figure 1 also
shows union density, the proportion of workers in manufacturing
covered by union contracts. From 1997 to 2006 the percentage of the
workforce covered by collective bargaining in manufacturing declined
by 4.8 percentage points.
Before developing a model to explain the determinants of labor’s
share, we first examine whether the decline in labor’s share is due
to declines in labor’s share within each state or to shifts in produc-
tion from states with high labor’s share to states with low labor’s
Figure 1
Labor’s Share and Union Density
Source: Annual Survey of Manufacturers and Census of Manufacturers and
http://www.unionstats.com/ Barry T. Hirsch and David A. Macpherson.
Do Unions Affect Labor’s Share of Income 795
share. We will also examine whether the decline in union density is
due to lower density within states or to shifts in employment of
production workers from states with high union density to states
with low union density. If it turns out that almost all of the decline
in labor’s share of income is due to shifting production from states
with higher values of labor’s share to states with lower values of
labor’s share, then there would not be much point in developing a
model to explain the decline in labor’s share of income. Similarly, if
the decline in unionization were caused primarily by the shifting of
jobs from unionized states to non-unionized states, then using
unionization to explain a decline in labor’s share of income would
be spurious.
To decompose the change in labor’s share (DLSt) from period tto
t-kwe use the following equation for the 50 states and the District
of Columbia:
ΔΔΔΔΔLS LS q LS q LS q
titk
i
it it
i
it k it
i
it
=⋅+⋅+⋅
−
==
−
=
∑∑∑
1
51
1
51
1
51
(1)
The first term on the right hand side measures the effect of the shift
in production from one state to another on labor’s share of income
where LSit-kis labor’s share in state iat period t-kand Dqit is the
change in the share of output for state ifrom period tto period t-k.
The second term measures changes in labor’s share within states
where DLSit is the change in labor’s share for state ifrom period tto
period t-k, and qit-kis the share of output from state iat period t-k.
The third term measures the interaction of the “between states factor”
and the “within states factor,” or the covariation between the changes
in the composition of output between states and the changes in labor’s
share within states. Similarly, to decompose the change in unioniza-
tion from period tto period t-k, we use the following equation for
the 50 states and the District of Columbia, where Utis union density
and eit is the proportion of production workers employed in state iat
time t.
ΔΔΔΔΔUUe Ue Ue
titk
i
it it
i
it k it
i
it
=⋅+⋅+⋅
−
==
−
=
∑∑∑
1
51
1
51
1
51
(2)
796 The American Journal of Economics and Sociology
The results of both decompositions are shown in Table 1. From
1997 to 2006, labor’s share in manufacturing declined by approxi-
mately 3.6 percentage points, and nearly 90 percent of the decline was
accounted for by changes in labor’s share within each state. In
contrast, only 2 percent of the decline was due to shifts in production
between states. With respect to union density, virtually the entire 4.8
percentage point decline in union density was explained by declines
in unionization within states. Except for Iowa, Mississippi, North
Carolina, and Massachusetts, all states and the District of Columbia
experienced declines in union density. Since the declines in labor’s
share and unionization are both explained primarily by changes
within states, we can now move to the development of a model to
explain labor’s share of income.
The Model
The basic model used in this paper is an extension of the model
developed by Cowling and Waterson (1976) and is also similar to the
model used by Henley (1987). Assume a profit-maximizing firm exists
in an oligopolistic industry with Nfirms producing a homogeneous
product. Profit for the ith firm can be written as follows:
π
ii i
pq c q F=− −() (3)
where piis the profit, qiis output, and pis price and represents fixed
costs. The inverse demand function is:
Table 1
Decomposition of Changes in Labor’s Share and Union
Density 1997–2006
Labor’s Share Union Density
Changes Between States 2.1% -0.4%
Changes Within States 89.7% 100.5%
Covariance Term 8.1% -0.2%
Total Change -3.6% -4.8%
*Percentages in the first three rows do not sum to 100 because of rounding.
Do Unions Affect Labor’s Share of Income 797
pfQ gqq q
N
==( ) ( , ... )
12 (4)
The first order conditions for profit maximization are:
d
dq
dp
dQ
Q
qqp
dc
dq
i
ii
i
i
π
=∂
∂+− =0(5)
The partial derivative of Qwith respect to qiis a measure of collusion
among firms. To simplify matters, we follow Henley (1987) and
assume a Cournot type conjecture, i.e., ∂Q/∂qi=1, which implies that
firms act independently. Also following Henley (1987), we assume a
production function that is linearly homogeneous. However, rather
than having two factors of production (labor and capital), we assume
output is a function of production labor, non-production labor, and
capital so that qi=h(LP,Ln,K) where Lpis the number of production
workers, Lnis the number of non-production workers, and Kis the
amount of capital. By assuming that the production function is linearly
homogeneous, we can use Euler’s theorem, which states that output
can be decomposed into the sum of the marginal product of each
factor of production times the quantity of that factor along with the
assumption that firms set their marginal revenue products equal to
factor prices to maximize profits, thus allowing us to rewrite Equa-
tion (5) as follows:
pdc
dq pdQ
dp q
wL wL rK
ii
p
i
pni
ni
−=−
+
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
++
⎡
⎣⎤
⎦
1(6)
where wpis the wage rate for production workers, wnis the wage rate
for non-production workers, and ris the cost of capital. Assuming that
each firm produces the same level of output, if we multiply both sides
of Equation (6) by qiand multiply the numerator and denominator on
the right hand side by 1/Qand sum, we get the following:
pq dc
dq qNwL wL rK
i
i
N
i
i
i
N
pp nn
==
∑∑
−=
−
⎡
⎣
⎢⎤
⎦
⎥++
[]
11
1
1
η
(7)
798 The American Journal of Economics and Sociology
where his the elasticity of demand and LL
i
p
i
N
p
=
∑=
1
LL KK
i
n
i
N
ni
i
N
==
∑∑
==
11
. From this, it is easy to see that labor’s share of
income is:
wL
YwL
wL N
wL
wL
rK
wL
pp
nn
pp
nn
pp pp
=
++
−++
⎡
⎣
⎢⎤
⎦
⎥
⎛
⎝
⎜⎞
⎠
⎟
1
11
11
η
(8)
where Yis valued added. Equation (8) implies that labor’s share of
income is a decreasing function of the ratio of Ln/Lpand of K/Lpand
an increasing function of N and h. Moreover, following Cowling and
Waterson (1976), it can be shown that 1/(Nh-1) =L/(1 -L), where L
is the Learner index of concentration. So, as the number of firms in an
industry or the elasticity of demand goes down (demand becomes
more inelastic), industry concentration increases, which in turn results
in an increase in the price-cost margin and a decrease in labor’s share
of income.
Empirical Model, Data, and Results
Based on the model in Equation (8), we propose to estimate the
following equation:
LS
K
L
L
Linvship union
it
pit
n
p
it
it
()
=
+⎛
⎝
⎜⎞
⎠
⎟+⎛
⎝
⎜⎞
⎠
⎟++
ββ β β β
01 2 3 4 iit it it
export u++
β
5
(9)
Data on capital stock by state were published in the CM only for
1997. We estimate the capital stock for the years 1998–2006 as follows:
KgK
nc
nc
t
it t i
i
it
it
i
=+
()
⎛
⎝
⎜⎞
⎠
⎟
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
=
=
=
∑∑
11
1997
1
51
1
51
,9998 2006−(10)
where Kit is the real capital stock in state iat time t,Ki,1977 is the capital
stock in the ith state in 1997, gtis the growth rate in the real capital
Do Unions Affect Labor’s Share of Income 799
stock in manufacturing using a Bureau of Economic Analysis chain-
type quantity index for the net stock of private fixed assets in
manufacturing, and ncit is the new capital expenditures in state iat
time t.
The first variable in Equation (9) is K/Lp, which is the ratio of the
capital stock in manufacturing to employment of production workers
in manufacturing where Kis the capital stock in state iat time t
(dropping the subscripts) and Lpis the number of production workers
in state iat time t, both from the ASM and the CM. Since labor’s share
of income is a decreasing function of K/Lp, as shown in Equation (8),
we expect b1to be negative. The second variable in Equation (9) is
Ln/Lpthe ratio of non-production to production labor. Once again, as
shown in Equation (8), labor’s share of income is a decreasing func-
tion of Ln/Lpso we expect b2to be negative. The variable invship is the
ratio of inventories to shipments in state iat time t. This variable is
included to control for cyclical changes. We expect b3to be positive
because when the ratio of inventories to shipments rises, production
is outstripping sales, and that in turn squeezes profits, resulting in an
increase in labor’s share of income.
The union variable is the proportion of workers covered by a
collective bargaining agreement. If unions have no impact on labor’s
share of income, b4will be equal to zero. Conversely, if unions have
a positive impact on labor’s share, b4will be positive.
Finally, we include the variable export in Equation (9), which is the
ratio of exports to current Gross Domestic Product (GDP) in state iat
time t. This variable is a proxy for market power. Most exports come
from the manufacturing sector, which is generally more concentrated
than non-manufacturing sectors. So, states with a high proportion of
their output in the form of exports will generally have higher levels of
concentration, and as the ratio of exports to GDP increases, market
concentration increases. Other things being equal, an increase in
market concentration will reduce labor’s share of income. Therefore,
we expect b5to be negative.
Table 2 shows the mean values of the dependent and indepen-
dent variables by state for each year. We use three measures of
labor’s share of income. The first measure of labor’s share of income
(LS1) is:
800 The American Journal of Economics and Sociology
LS W
VA
p
1=(11)
where Wpis wages paid to production workers and VA is value added.
Many would argue that this definition of labor’s share of income is
too narrow because it does not take into account fringe benefits. The
ASM and CM started collecting data on fringe benefits in 1967.
Unfortunately, they do not provide fringe benefit data for production
and non-production workers separately. Thus, we need to estimate
the value of fringe benefits provided to production workers.
The first method for estimating benefits is to assume that benefits
are distributed proportionately among all employees, i.e., all worker
ranks receive the same benefits. Under this assumption, the appro-
priate definition of labor’s share of income (LS2) is as follows:
LS
WFL
LL
VA
p
p
pn
2=+⋅ +(12)
where Wpis wages paid to production workers, Fis the total value of
fringe benefits, Lpis the number of production workers, Lnis the
Table 2
Mean Values
Year LS1 LS2 LS3 K/LpLn/Lpinvship union exports
1997 0.190 0.248 0.239 0.139 0.388 0.111 0.159 0.658
1998 0.191 0.247 0.239 0.148 0.384 0.112 0.158 0.612
1999 0.186 0.247 0.239 0.166 0.388 0.111 0.160 0.615
2000 0.187 0.254 0.244 0.180 0.386 0.111 0.150 0.643
2001 0.190 0.258 0.260 0.204 0.407 0.118 0.142 0.590
2002 0.185 0.241 0.233 0.231 0.422 0.108 0.132 0.550
2003 0.178 0.235 0.226 0.254 0.435 0.104 0.132 0.550
2004 0.168 0.222 0.214 0.277 0.434 0.097 0.126 0.585
2005 0.157 0.208 0.200 0.294 0.432 0.095 0.123 0.627
2006 0.155 0.207 0.199 0.310 0.416 0.098 0.118 0.699
Do Unions Affect Labor’s Share of Income 801
number of non-production workers, and VA is value added. This
measure of labor’s share may overestimate the benefits received by
production workers because higher paid non-production workers
tend to get more vacations, bonuses, and other fringe benefits not
afford to production workers.
The second method for estimating benefits is to assume that they
are proportionate to payroll, i.e., all workers receive fringe benefits
that are equal to a fixed proportion of their wages. In this case, labor’s
share of income (LS3) would be measured as follows:
LS
WF W
WW
VA
p
p
pn
3=+⋅ +(13)
where Wnis the wages of non-production workers.
Equation (9) is estimated using a fixed effects model because the
unit of observation is a large geographical area. This allows us to hold
constant unobserved heterogeneity between states (Wooldridge 2009).
Table 3 presents estimates of Equation (9) using LS1, LS2, and LS3 as
measures of labor’s share of income. Column 2 presents fixed effects
estimates of Equation (9) where labor’s share is measured using LS1.
The coefficients for the capital-labor ratio, the ratio of non-production
to production workers, the ratio of inventories to shipments, and the
ratio of exports to state GDP all have the expected signs. We estimate
robust standard errors and find that all of the aforementioned variables
are statistically significant at the 0.01 level or better. The coefficient of
the union variable is 0.0931 and is also statistically significant at the
0.01 level. Thus, we reject the null hypothesis that unions do not have
an impact on labor’s share of income. The implication of the positive
sign of the union variable is that higher levels of unionization are
associated with a larger share of income for labor.
The equation in column 3 estimates the same model defining labor’s
share as LS2. Again, the coefficients of the capital labor ratio, the ratio
of non-production to production workers, the ratio of inventories to
shipments, and exports all have the expected signs and are statistically
significant at the 0.01 level or better. Most importantly, the coefficient
of the union variable is 0.105 and is statistically significant at the 0.05
level.
802 The American Journal of Economics and Sociology
The equation in column 4 provides an alternative measure of labor’s
share using LS3. Again, the coefficients of the capital labor ratio, the
ratio of non-production to production workers, the ratio of inventories
to shipments, and exports all have the expected signs and are all
statistically significant at the 0.01 level or better. The coefficient of the
union variable is 0.132 and is statistically significant at the 0.01 level.
The estimates of Equation (9) using various definitions of labor’s
share are consistent and clearly reject the null hypothesis that unions
do not have an impact on labor’s share of income. The estimated
coefficients for different definitions of labor’s share range between
0.931 and 0.132.
Table 3
Regression Results
LS1 LS2 LS3
K/Lp-0.076*** -0.079** -0.071**
(3.485) (2.852) (2.473)
Ln/Lp-0.151*** -0.178*** -0.182***
(8.222) (8.525) (8.478)
invship 0.560*** 0.694*** 0.724***
(4.651) (4.703) (4.512)
union 0.093** 0.105* 0.132**
(2.416) (2.190) (2.448)
export -0.027*** -0.031*** -0.042**
(3.499) (3.143) (2.747)
_cons 0.201*** 0.254*** 0.247***
(11.362) (11.888) (10.961)
r2_w 0.495 0.450 0.272
r2_o 0.289 0.289 0.227
r2_b 0.116 0.139 0.142
sigma_u 0.031 0.037 0.038
sigma_e 0.017 0.022 0.033
rho 0.763 0.747 0.573
*p <0.05, **p <0.01, ***p <0.001 using 1 tailed tests.
Do Unions Affect Labor’s Share of Income 803
From 1997 to 2006, using un-weighted averages across states,
labor’s share declined 3.6 percentage points. The un-weighted average
is calculated as follows:
LS n
W
VA
uw
p
i
n
i
11
1
=⎛
⎝
⎜⎞
⎠
⎟
=
∑(14)
The decline in unionization explains 10.7 percent of this decline.
Again, using un-weighted averages LS2 declined 4.1 percentage
points, and the decline in unionization explained 10.5 percent of this
decline. Finally, using un-weighted averages for LS3, labor’s share
declined 4.0 percentage points, and declining unionization explained
13.4 percent of this decline.
Alternatively, one may use a weighted average of labor’s share to
measure the decline in labor’s share and the decline in unionization.
Equation (15) shows that a weighted average is the equivalent of using
aggregate time-series data.
LS W
VA
VA
VA
W
VA
wi
p
i
i
ni
i
i
n
i
p
i
n
i
i
1
1
1
1
=⎛
⎝
⎜⎞
⎠
⎟
⎛
⎝
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
=
=
=
=
∑∑
∑
==
∑
1
n(15)
From 1997 to 2006, when one uses time-series data, one finds that
LS1 declined 3.2 percentage points and that declining unionization
explained 12.9 percent of this decline. Over the same time period,
the time-series measure of LS2 and LS3 declined by 3.9 and 3.8
percentage points, respectively. The decline in unionization
explained 12.4 percent of the decline in LS2 and 16.2 percent of the
decline in LS3.
Table 4 shows the actual (weighted and un-weighted) and predicted
values of labor’s share of income using LS1. The predicted values are
calculated by substituting the mean values of the independent vari-
ables from Table 2 into the equation for LS1 reported in Table 3.
Finally, the last column of Table 4 shows what labor’s share of income
would have been had the level of unionization remained constant at
its 1997 level. Looking at the data in Table 4, one can see that the
804 The American Journal of Economics and Sociology
regression does a fairly good job in predicting the decline in labor’s
share (values for LS2 and LS3 are shown in Appendix 1 and 2,
respectively).
Figure 2 shows the difference between the predicted value of
labor’s share taking into account the decline in unionization and the
predicted value assuming that unionization had remained at its 1997
level. The graph shows that even in the absence of a decline in union
coverage there would have been a substantial decline in labor’s share
of income. However, the fact that the two lines are getting further
apart shows that decline in unionization certainly contributed to the
decline in labor’s share.
In 1997 the model for LS1 predicts that labor’s share would be 19.1
percent. By 2006 the model predicts that labor’s share would be 16.2
percent. However, if the level of unionization had remained at its 1997
level then the model predicts that labor’s share would have been 16.6
percent. Another way to interpret these findings is to recognize that
with the decline in unionization, the model predicts that labor’s share
would decline by 15.4 percent whereas had unionization remained at
its 1997 level, labor’s share would have declined by only 13.4 percent.
Table 4
Actual and Predicted Values of Labor’s Share (LS1)
Year Weighted Unweighted
Predicted
Value
Holding Unionization
Constant
1997 0.185 0.190 0.191 0.213
1998 0.185 0.191 0.193 0.214
1999 0.182 0.186 0.190 0.212
2000 0.184 0.187 0.188 0.210
2001 0.185 0.190 0.188 0.211
2002 0.178 0.185 0.178 0.202
2003 0.172 0.178 0.172 0.195
2004 0.163 0.168 0.165 0.189
2005 0.149 0.157 0.161 0.186
2006 0.153 0.155 0.162 0.187
Do Unions Affect Labor’s Share of Income 805
Thus, the decline in unionization between 1997 and 2006 explains
about 12.9 percent of the decline in labor’s share of income.
Summary and Conclusion
The results presented in this paper show that unions have a positive
impact on labor’s share of income. While labor’s share of income
would have declined in the absence of a decline in unionization, it is
clear that the falling levels of unionization contributed to the decline
in labor’s share, and that the impact of declining unionization has
grown over time. Specifically, we find that for each 1-percentage point
reduction in union density the proportion of income received by
production workers declines by between 0.09 and 0.13 percentage
points depending on the particular definition of labor’ s share used,
holding other factors constant. In addition, we find that the decline in
unionization between 1997 and 2006 explains between 10 and 16
percent of the decline in labor’s share.
Early time series studies that have examined the impact of unions
on labor’s share of income were primarily descriptive. They generally
seem to find that unions did not have an impact on labor’s share of
Figure 2
Impact of Declines in Unionization on Labor’s Share
806 The American Journal of Economics and Sociology
income. In contrast, later studies have relied primarily on cross-section
data and here the results have been mixed, although most studies
seem to indicate that unions do have a positive impact on labor’s share
of income.
This study adds to our understanding of this topic by first devel-
oping an analytical model based on imperfect competition, and then
using it with panel data to test the hypothesis that social and insti-
tutional forces play an important role in determining the distribution
of income. While a number of economists have argued that labor’s
share of income is constant, this conclusion is largely based on
defining labor as any employee who receives some form of com-
pensation. This approach prevents economists from making mean-
ingful social distinctions between different forms of human activity.
Thus, a CEO and a janitor are both considered “labor.” This study
shows that such an approach to defining labor masks significant
changes that have taken place in the distribution of income in
recent years.
Most importantly, this study supports the view that social and
institutional forces play an important role in determining the distribu-
tion of income between labor and capital. This finding implies that
public policy can play an important role in determining the distribu-
tion of income, a finding that is consistent with DiNardo, Fortin, and
Lemieux (1996). They found that labor market institutions, and hence
public policy, help to explain changes in the distribution of wages in
the U.S.
One of the limitations of this study is that it considers changes in
labor’s share only for the U.S. manufacturing sector. In the future, it
would be useful to develop a measure of wages that would measure
the share of income received by production and non-supervisory
workers in the U.S. economy to see if the results found in the U.S.
manufacturing sector hold for the U.S. economy as a whole.
A major policy implication of this study is that passage of legislation
to promote the unionization of workers, such as the Employee Free
Choice Act, could have a significant impact on the distribution of
income between labor and capital. This Act would allow workers to
form unions by signing authorizing cards and provide for arbitration
in disputes involving first contracts.
Do Unions Affect Labor’s Share of Income 807
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Do Unions Affect Labor’s Share of Income 809
Appendix 1
Actual and Predicted Values of Labor’s Share (LS2)
Year Weighted Unweighted Predicted Value
Holding Unionization
Constant
1997 0.243 0.248 0.248 0.248
1998 0.241 0.247 0.250 0.250
1999 0.236 0.247 0.247 0.247
2000 0.240 0.254 0.244 0.245
2001 0.244 0.258 0.245 0.246
2002 0.234 0.241 0.233 0.236
2003 0.228 0.235 0.226 0.229
2004 0.217 0.222 0.218 0.221
2005 0.200 0.208 0.214 0.218
2006 0.204 0.207 0.215 0.219
Appendix 2
Actual and Predicted Values of Labor’s Share (LS3)
Year Weighted Unweighted Predicted Value
Holding Unionization
Constant
1997 0.233 0.239 0.240 0.261
1998 0.231 0.239 0.242 0.262
1999 0.227 0.239 0.240 0.259
2000 0.230 0.244 0.236 0.257
2001 0.233 0.260 0.238 0.256
2002 0.225 0.233 0.226 0.242
2003 0.218 0.226 0.219 0.235
2004 0.208 0.214 0.210 0.228
2005 0.191 0.200 0.206 0.226
2006 0.195 0.199 0.206 0.229
810 The American Journal of Economics and Sociology
