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A joint initiative of Ludwig-Maximilians University’s Center for Economic Studies and the Ifo Institute for Economic Research
Area Conference on
Global Economy
11 - 12 February 2011 CESifo Conference Centre, Munich
International Trade and Income Distribution:
The Effect of Corporate Governance Regimes
Hartmut Egger, Peter Egger and Douglas Nelson
CESifo GmbH
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81679 Munich
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International Trade and Income Distribution:
The Effect of Corporate Governance Regimes
Hartmut Egger,∗ Peter Egger† and Douglas Nelson‡
December 1, 2010
Abstract
This paper presents an analysis of the way corporate governance regimes mediate the
effect of international trade on income distribution.
Key words: Governance; Profit sharing; International trade
JEL classification: F14; F15
Acknowledgement: To be added. Peter Egger acknowledges funding from the Austrian
Science Fund through grant P17713-G05.
∗
Affiliation: University of Bayreuth, CESifo, and Leverhulme Centre for Research on Globalisation and Economic Policy, School of Economics, University of Nottingham. Address: University of Bayreuth, XXX. E-mail:
XXX. Phone: +49 (0)XXX.
†
Affiliation: ETH Zürich, CEPR, CESifo, WIFO, GEP, and OUCBT. Address: ETH Zürich, KOF, WEH E6,
Weinbergstrasse 35, 8092 Zürich, Switzerland. E-mail: [email protected]. Phone: +41 (0)44 632 4108.
‡
Affiliation: Murphy Institute, Tulane University; and Leverhulme Centre for Research on Globalisation and
Economic Policy, School of Economics, University of Nottingham. Address: Murphy Institute, 108 Tilton Hall,
Tulane University, New Orleans, LA 70118-5698. E-mail: [email protected]. Phone: 504-862-3235.
1
1
Introduction
Given the expansion of trade, migration, and capital flows, along with increasingly complex
global organization of production, it is not surprising that the last 30 years has seen a boom in
research on globalization. Furthermore, given the rapid rise in the skill premium, throughout
the OECD, over this period, it is probably not surprising that the great majority of this work
has focused on the link between globalization and labor markets. What is perhaps surprising is
how modest are the quantitatively estimated effects.1 In the face of widespread public concern
about various aspects of globalization, these results pose something of a problem. On the one
hand, the results may simply be correct and the non-economist public incorrect. On the other,
there are a variety of indirect channels via which globalization might be affecting the economy
in general, and labor markets in particular, and which are not picked up by the standard
methods used to identify those effects.2 This has led to work that has examined such indirect
channels as the effect of globalization on unions (Abowd and Lemieux, 1993; Baccaro, 2008;
Borjas and Ramey, 1995; Guadalupe, 2007) or the effect of globalization on the welfare state
(Hicks, 1999; Pontusson, 2005; Guadalupe, 2007; Swank, 2002). In both cases there is evidence
that globalization weakens these institutions, and further evidence that these institutions are
associated with more equal distribution of income.3 Thus these indirect effects seem a promising
avenue for research.
While labor market institutions and political institutions have been widely studied in this
context, corporate governance institutions have been much less widely studied.4 This is somewhat surprising since, not only are firms the most significant institution in the capitalist economy, but there is considerable evidence of both cross sectoral and cross national heterogeneity
in corporate governance institutions (Allen and Gale, 1999; Keasey, Thompson and Wright,
2005; Morck, 2005). This suggests that more systematic study of the way corporate governance
structures condition adjustment to globalization and the way corporate governance institutions
respond to globalization are potentially questions of considerable interest. We begin with a
brief overview of the general literature on corporate governance. In section 3 we describe our
theoretical framework in a closed economy and in section 4 we present open the economy to
trade and examine the effects of trade on income distribution as mediated by differing corporate
governance regimes.
2
Corporate Governance in General
A first issue is definitional: what exactly is ”corporate governance”? Probably the most common
definition in the corporate finance literature is the one given in the excellent survey of that
literature by Shleifer and Vishny (1997, pg. 737): “Corporate governance deals with the ways
in which suppliers of finance to corporations assure themselves of getting a return on their
investment”. This definition reflects the concern, central to corporate finance and research on
corporate governance more generally, that the separation of ownership and control, noted early
1
On the link between trade and wages see Slaughter (2000), for immigration and wages see Card (2009).
It is easy enough to see how this can happen. For example, consider the effect of trade on wages as mediated by
unions. Trade might well weaken unions, but need not do so in any way identified by mandated wage regressions.
That is, the sectoral pattern of weakening need not be correlated with changes in relative prices.
3
For the effect of unions on income distribution, see Freeman (1993), Card, Lemieux and Riddell (2004),
DiNardo and Lemieux (1996), or Fortin and Lemieux (1997). On the link between welfare state effort and income
distribution, see Huber and Stephens (2001) or Pontusson (2005).
4
It should be noted that, while this statement is true of economists and political scientists, researchers in law
and finance have devoted some considerable effort to corporate governance and the political economic links to
globalization.
2
2
on by Berle and Means (1937), should be a primary focus in research on the modern firm.
While this definition has the virtue of clarity of focus, a number of scholars have noted that
it may be excessively narrow. Rajan and Zingales (2000, see also Zingales 2000) note that,
increasingly, the Berle-Means firm competes with, or is even displaced by, alternative corporate
structures—especially in economically key service sectors. Allen and Gale (1999) argue that the
standard definition reflects too much the concerns of American scholars. They argue that in
many countries, this is an inaccurate representation of what is central to corporate governance.
For example, a system like Germany’s with co-determination explicitly empowers organized
labor; while managers in Japan assert a broader notion of “stakeholders”. These considerations
lead Tirole (2001, pg. 4) to propose a more expansive definition as: “the design of institutions
that induce or force management to internalize the welfare of stakeholders.” This leads directly
to a contract theoretic approach with a potentially broader range of agents. Zingales (1998)
proposes a closely related definition that more explicitly emphasizes conflicts: “[A] governance
system [is] the complex set of constraints that shape the ex-post bargaining over the quasi-rents
generated in the course of a relationship.” Like Tirole’s definition, Zingales contemplates a more
expansive notion of corporate governance than Shleifer and Vishny’s, but, in its emphasis on
quasi-rents, it seems potentially less expansive than that of Tirole. In this paper, we would like
to emphasize the fundamentally political relationship by referring to corporate governance as
the set of institutions that define and regulate the relations between insiders and outsiders in
the context of the firm.5 Among the obvious related parties are equity owners (various sorts),
debt holders (various sorts), managers, workers (senior/junior, union/non-union), suppliers, and
consumers.6 Comparative analysis makes quite clear that the identities of insiders and outsiders
vary considerably across countries. It would be surprising if such differences did not have
implications for the analysis of adjustment to globalization.
A second issue has to do with the conditions under which corporate governance might be
relevant. In a world of constant returns to scale, perfect competition, and complete and perfect
markets, there is obviously no role for corporate governance, even under the most expansive
definitions above.7 In a world with most standard distortions, while there may be a role for
government intervention, corporate governance issues still do not usually arise. Exceptions arise
in at least three sorts of case: informational distortions; missing markets; and politically/legally
induced asymmetries. The most obvious exception relates to informational distortions. These
distortions go to the heart of corporate governance issues. For Tirole and Zingales, as much as
for Shleifer and Vishny, a defining characteristic of insiders is that they possess information that
outsiders do not possess. In the corporate governance literature, the most common example is
managerial opportunism in the face of dispersed ownership Stein (2003). The idea is that it is in
no individual owner’s interest to acquire the relevant information. This leaves the manager free
to channel resources in ways that are not value maximizing. In the absence of an active market
for control, for example, there may be an incentive for individual owners to acquire large shares
of a corporation (i.e. become blockholders). It turns out that Europe has a much higher degree
5
Insiders have privileged access to power resources not available, or at least not available on the same terms, to
outsiders. These resources include, but are not limited to information and decision-making rights. For a similar
emphasis see: Hellwig (2000), Pagano and Volpin (2001), Rajan and Zingales (2003), and Barker and Rueda
(2007).
6
At some remove, of course, we also have the local community, which is straightforwardly affected by the
behavior of the firm; various levels of government that might make fiscal, and other, claims on the firm; auditors;
analysts; regulators; etc.
7
Allen and Gale (1999, Cptr. 5) note that in the perfectly competitive environment, decentralization has several
important implications, including: value maximization as an unambiguous objective for the firm; decentralization
of implementation of this objective to lower level managers; shareholder unanimity (i.e. all owners agree on this
objective); and irrelevance of capital structure (generalized Modigliani-Miller theorem).
3
of blockholding than does the US (Becht and Röell, 1999). This is often seen as a response to
weaker protection of equity owners in the face of managerial opportunism—via legal or market
mechanisms (Shleifer and Vishny, 1986).8 Second, Allen and Gale (1999) stress the importance
of incomplete markets to corporate governance. For example, with incomplete markets many of
the standard results that are extensions of the Arrow-Debreu model no longer hold.9 Third, and
particularly relevant for our analysis, the presence of unions creates insiders and outsiders in the
sense of Lindbeck and Snower (1988), but corporate governance is implicated in this relationship
as well. That is, it is clearly the case that corporate governance regimes across countries, and
to a lesser extent across classes of firms within countries or sectors, differentially empower labor
in governance decisions. For example, German law specifies that labor must be represented
on the both the supervisory board and the management board, while US law contains no such
requirements. Thus, union labor is rendered an insider in the German context and an outsider
in the US context. The logic of this case could, in principle, apply to any “stakeholder” however
distant (though politically well organized).10 For example, laws might privilege debt holders
relative to equity holders; making the former the insiders and the latter the outsiders. And, of
course, managers are virtually always insiders, with countries varying considerably in the extent
of protections granted to equity holders.11
3
A Simple Model of Corporate Governance in General Equilibrium
In this paper, we are ultimately interested in the way corporate governance regimes interact with
international trade. Specifically, we are interested in how differences in these regimes mediate
the distributional effects of trade. Our focus on the effects of economy-wide regimes suggests
that we should build on a general equilibrium framework. However, our interest in corporate
governance suggests that we will need a model with equilibrium profits. To generate such profits
and retain tractability, we adopt a simplification in the spirit of Neary’s (2003; 2009) theory
of generalized oligopolistic equilibrium (GOLE). As in Neary, we also apply the continuumquadratic preferences developed in those papers for their tractability and aggregation properties.
Unlike Neary, since we are only interested in the presence of profits, where Neary’s model involves
a continuum of oligopolistic sectors, we will simply have a continuum of monopolistic sectors.
As we have already noted, the corporate governance relationship is complex: the number
of potential stakeholders is large; these stakeholders are related in a variety of both statutory
and non-statutory ways that vary across economies. Our minimalist approach to the corporate
governance problem involves modeling governance as a relationship between owners, managers
and workers.12 Furthermore, while this might involve issues such as the nature of takeover rules,
8
It should be noted, however, that it has proved hard to find evidence of economically significant impacts of
blockholders Holderness (2003).
9
Relative to footnote 7, Allen and Gale (1999) sketch the argument that all four of the implications can fail
with incomplete markets, and then develop a systematic analysis of these implications through the remainder of
the book.
10
Hellwig (2000) and Pagano and Volpin (2005) both develop political economic analysis in which it is precisely
management and labor (the insiders) that exploit owners (the outsiders).
11
These last two points make clear the difference between positive analysis of the sort sketched here and the more
normative component of the Grossman-Hart-Moore type of analysis (Grossman and Hart, 1986; Hart, 1995a; Hart
and Moore, 1990). That is, arrangements empowering stakeholders may well be inefficient in the allocation of
risk and decision-making power. Our concern is with the implications for outcomes in equilibrium of any given
arrangement.
12
Part of the reason for abstracting from Neary’s focus on oligopoloy is that the presence of oligopolistic
interaction would lead to additional complexity in the relationship between owners and managers that simply
4
board size, etc., we focus on two major elements: compensation of managers; and the presence
or absence of labor representatives on the board. We collapse the complicated relationship
between management and labor into the bargain between management and labor over the wage,
which we see as representing the more general relationship in our simple model economies.
The great majority of research on corporate governance is essentially microeconomic (e.g.
Jensen and Meckling, 1976; Hart, 1995b). That is, this work focuses on the implications of the
contract/information structure of the firm for efficiency of that firm and the distribution of the
proceeds of production by that firm. By contrast, we will be interested here in the implications
of economy-wide corporate governance regimes. The fields of law, political science and finance
have extensively studied differences in such regimes, and their implications, under the broad
lable of comparative corporate governance.13 One of the sytlized facts that is common to all of
this research is the existence of two archetypal regimes. Depending on the particular focus of
the research, these archetypes go under a variety of labels: shareholder v. stakeholder economies
(Letza, Sun and Kirkbride, 2004); common law v. civil law (La Porta, Lopez-De-Silanes, Shleifer
and Vishny, 1998); liberal v. coordinated market economies (Hall and Soskice, 2001); etc. Another way of making the distinction is with reference to the two countries whose corporate
governance regimes most closely approximate the archetypes: Anglo-American v. German.14
Thus, the US is generally taken as the exemplar of the shareholder/common law/liberal market
economy. Corporate governance in such an economy is characterized by: strong emphasis on
shareholder value as the unique objective of management (i.e. managers have a fiduciary duty to
shareholders); separation of ownership and control; active market for corporate control including
relatively easy hostile takeover; and extensive protections for minority shareholders with relative
unimportance of block-holders. By contrast, Germany is generally taken as the exemplar of the
stakeholder/civil law/coordinated market economy. Corporate governance in such economies
is characterized by: an explicit commitment to stakeholders beyond shareholders; the general
presence of blockholders (thus reducing the separation of ownership and control); relatively thin
market for equities with a much larger role for banks; and weak protection of minority shareholders. Of particular importance in supporting the stakeholder orientation of the German system
is the dual board structure. The management board (the vorstand ) oversees the day to day
management of the firm, while the supervisory board (the Aufsichtsrat) appoints and oversees
the management board, must approve major capital and strategic decisions, sets managerial
compensation, approves the dividend, and approves the company accounts (Charkham, 2005,
chapter 2).
One central element of Germany’s stakeholder regime is the role of labor in co-determination
of firm decisions. There are two central pillars of co-determination: representation of labor
on the supervisory board; and firm-level works councils in the context of sector-level wage
bargaining.15 These governance institutions increase both the relative power of labor in bargains
with the firm; and increase the channels for communication and the stake of labor in the firm.
In the language of Freeman and Medoff (1984), then, co-determination increases the effectiveness
detracts from the governance relationship that is the focus of this paper.
13
Representative work in Economics includes Allen and Gale (2000) and the papers in Morck (2005); in Finance
Franks and Mayer (1990) and LaPorta et al. (1998; 2000); in Law Roe (2003) and Coffee (2001); and in Political
Science Gourevitch and Shinn (2005).
14
The literature comparing the US and Germany is huge. For a recent analysis, focused on corporate governance
in particular, see O’Sullivan (2000).
15
It is interesting to note that, while Germany is a particularly strong example of such co-determination, a
number of countries share many of the same traits. In particular, like Germany, Austria and Denmark have a
dual board system with labor representation on the supervisory board; and while Norway and Sweden do not
have dual boards, labor is represented at the board level. See Jackson (2005) for a discussion of these differences
and an attempt to account for them.
5
of both the monopoly and the collective voice faces of labor organization. The overall effect
on the productivity and distribution have been matters of considerable empirical interest.16
This empirical research is plagued with difficult data problems, but, to the extent that one can
draw a broad judgment from this literature, it seems that co-determination has little observable
effect on productivity, but that profits are reduced, both relative to similar firms without codetermination. The model to follow has exactly this property. That is, between our two
regimes (a ”US” regime and a ”German” regime), the presence of labor on the board will result
in a lower share to capital, but there will be no effect on productivity.
Ours is far from the first paper to look inside the firm for ways to understand economywide
response to globalization.
Over the last ten years or so a sizable literature has developed
examining how firm organization interacts with globalization to affect aggregate patterns of
trade and the distribution of the benefits from trade (for surveys see Helpman, 2006; Antràs
and Rossi-Hansberg, 2009). This line of research, whether deriving from the transactions cost
approach (e.g. Ethier, 1986; McLaren, 2000; Grossman and Helpman, 2002) or the property rights
approach (e.g. Antràs, 2003; Antràs, 2005; Antràs and Helpman, 2004), is primarily focused on
the organization of production and its effect on trade. By contrast, our focus is on corporate
governance and how governance regimes interact with trade. That is, our interest is in the effect
of rules of general applicability and not the internal microecnomic details of contracting. Thus,
our concerns are closer to those papers which focus on differences in labor market regimes (e.g.
Davis, 1998) or matching in an environment with sub- and super-modular technologies where
countries differ in the skill distribution of workers (e.g. Grossman and Maggi, 2000).
In this section, we briefly describe the main model assumptions and characterize the equilibrium outcome in a closed economy. The following section considers international trade.
3.1
Endowments, technology and preferences
We consider an economy that is populated by two groups of individuals, workers and capital
owners. Capital owners are identical and hold an equal share of firms in either industry.17 Firms
are equally distributed across sectors and the total number of competitors, 𝑁 , is exogenous.
Firms do not differ in their technology. They hire one manager and have to employ one unit of
labor for each unit of output, they produce. There are no fixed costs. The economy is populated
by 𝐸 workers, each of them endowed with one unit of labor. Workers are ex ante identical but
end up performing different tasks. 𝑁 workers are employed as managers, while 𝐿 = 𝐸 − 𝑁
workers are used as variable labor input.
Workers and capital owners add up to the overall mass of consumers. Consumers have
identical quasi-homothetic preferences that are represented by the quadratic utility function
]
∫ 1[
1
𝑢=
𝑎 − 𝑥(𝑧) 𝑥(𝑧)𝑑𝑧 − 𝐼𝑣(𝑔),
(1)
2
0
where 𝑎 is a preference parameter, 𝑥(𝑧) is the consumption level of goods from industry 𝑧, 𝐼 is
an indicator function, which equals 1 if the individual is a manager and 0 otherwise, and 𝑣(𝑔) is
the disutility of managers from exerting effort in wage-employment negotiations with firm-level
unions (see below). Consumers maximize utility (1), subject to their budget constraint
∫ 1
𝑝(𝑧)𝑥(𝑧)𝑑𝑧 ≤ 𝑚,
(2)
0
16
Goergen, Manjon and Renneboog (2008) is a good overall survey of current research on German corporate
governance. Several recent papers provide convenient surveys of the work specifically addressing the productivity
and distributional effects of co-determination: Renaud (2007), Petry (2009), and Bermig and Frick (2010).
17
This assumption is not critical, but simply ensures a positive income level of capital owners even in the
absence of any transfer payments.
6
where 𝑚 is individual income and 𝑝(𝑧) is the price of good 𝑧. The solution to the utility
maximization problem is represented by demand function 𝑥(𝑧) = 𝑎 − 𝜆𝑝(𝑧), where 𝜆 denotes
the consumer’s marginal utility of income, which depends on her level of income,
∫ 1 𝑚, and the
first as well as the second (uncentered) moment of the price distribution, 𝜇1 = 0 𝑝(𝑧)𝑑𝑧 and
∫1
𝜇2 = 0 𝑝(𝑧)2 𝑑𝑧, respectively. To be more specific, we have
𝜆=
𝑎𝜇1 − 𝑚
.
𝜇2
(3)
In the interest of notational simplicity, we have neglected consumer indices in Eqs. (1)-(3).
However, it is clear that in general agents can differ in imcome, 𝑚, their marginal utility of
income, 𝜆, and demand, 𝑥(𝑧). Adding up 𝑥(𝑧) over all individuals and solving for 𝑝(𝑧) gives
inverse industry demand
1
𝑝(𝑧) = [𝑎 − 𝑏𝑋(𝑧)] ,
(4)
Λ
where 𝑋(𝑧) is aggregate demand for good 𝑧, 𝑏 equals one over the mass of consumers, and Λ
denotes the representative consumer’s marginal utility of income, which is defined in analogy to
(3) and given by
𝑎𝜇1 − 𝑏𝑀
Λ=
,
(5)
𝜇2
with 𝑀 denoting aggregate income. In the following, we choose indirect utility of the representative consumer as the numeraire and set Λ = 1.
3.2
Labor market institutions
In our model, industries differ in their labor market institutions. To be more specific, we assume
that in a subset of industries 𝑧¯ ∈ (0, 1) unions are organized at the firm-level, while in the
residual industries the labor market is competitive. Similar to Bastos and Kreickemeier (2009),
we rank industries such that unions are active in all 𝑧 ∈ [0, 𝑧¯] industries. In these industries,
firms and unions jointly determine employment and wages by maximizing the following Nash
product
𝑁 𝑃𝑖 = [(𝑤𝑖 − 𝑤𝑐 )𝑞𝑖 ] [𝜋𝑖 ]𝛽 ,
(6)
where 𝑖 is a firm index, 𝑤𝑐 denotes the wage paid by firms in the 1−¯
𝑧 industries with a competitive
labor market, 𝑞𝑖 is output (or employment) at the firm level, and 𝜋𝑖 refers to operating firm-level
profits.18 Parameter 𝛽 ≥ 0 refers to the relative
bargaining strength of the firm. Substituting
∑𝑁
the goods market clearing condition 𝑋 = 𝑗=1 𝑞𝑗 in (4), operating profits can be written as
⎛
⎞
𝑁
∑
𝑏
𝜋 𝑖 = ⎝𝑎 −
𝑞𝑗 ⎠ 𝑞𝑖 − 𝑤𝑖 𝑞𝑖 .
2
(7)
𝑗=1
Substituting the latter into (6) and maximizing the resulting expression for 𝑤𝑖 and 𝑞𝑖 , gives
𝑤𝑖 = 𝑤 𝑐 +
𝑞𝑖 =
18
1 𝑎 − 𝑤𝑐
≡ 𝑤,
1+𝛽 𝑁 +1
𝑎 − 𝑤𝑐
≡ 𝑞.
𝑏(𝑁 + 1)
The sector index has been neglected in the interest of notational simplicity.
7
(8)
(9)
We can now compare (8) and (9) to the respective values in industries with a competitive labor
market. Thereby, we find that the labor market regime has no bearing on output, i.e. 𝑞 = 𝑞 𝑐
while wages are higher in unionized sectors, i.e. 𝑤 > 𝑤𝑐 due to rent-sharing a the firm-level.
This outcome is intuitive, as with efficient bargaining and a rent-oriented union, the bargaining
surplus is maximized by negotiating the efficient output level, whereas the distribution of the
bargaining surplus is determined by the negotiated wage rate, which depends on the relative
bargaining strength of the two parties.
Substituting (8) and (9) in (4) and (7), further implies
𝑎 + 𝑁 𝑤𝑐
,
𝑁 +1
(
)
𝛽
𝑎 − 𝑤𝑐 2
𝜋𝑖 =
≡ 𝜋.
𝑏(1 + 𝛽) 𝑁 + 1
𝑝=
(10)
(11)
Summing up, we can conclude that the outcome of firm-union bargaining is (second-best) efficient, since it does not distort sectoral output or prices, but just determines how the bargaining
surplus is distributed between the two bargaining parties. The larger the bargaining power
of capital owners, 𝛽, the larger is this group’s return from an agreement. Formally, we have
𝑑𝜋/𝑑𝛽 > 0, 𝜋 = 0 if 𝛽 = 0, and lim𝛽→∞ 𝜋 = 𝜋 𝑐 .
3.3
Manager contracts and rent extraction
Each firm needs to hire a manager prior to starting operation. In industries with a acompetitive
labor market, the manager simply runs the firm. In unionized industries, the manager additionally participates as the firm’s representative in the wage-employment negotiations with the
union. Crucially, the manager can influence the relative bargaining power of the firm, 𝛽, by her
effort in the wage-employment negotiation. We denote the manager’s effort by 𝛾 ∈ [0, 1) and
set 𝛽 ≡ 𝛾/(1 − 𝛾).19 Firms offer a contract to the manager that determines both the salary
and the effort in the wage bargain. To be accepted, this contract must fulfill the manager’s
participation constraint. In the interest of tractability, we abstract from problems associated
with information asymmetry in a principal-agent context and assume that managerial effort is
perfectly observable. In this case, an agent will accept the offer if the utility from acting as a
manager is at least as high as the expected utility from being employed as a production worker.
Furthermore, since capital owners do not have an incentive to over-compensate the manager,
they offer a contract that renders the manager indifferent between accepting and declining the
contract. In view of (1), the indifference condition (i.e. the binding participation constraint of
managers) is represented by the implicit function
[ (
)
(
) ]
(
)
1
𝑤 2
𝑤𝑐 2
1
𝑠 2
Γ(𝑠, 𝛾) ≡
𝑧¯ 𝑎 −
+ (1 − 𝑧¯) 𝑎 −
−
𝑎−
− 𝑣(𝛾) = 0,
(12)
2
𝑝
𝑝
2
𝑝
where 𝑧¯ and (1 − 𝑧¯) denote the probabilities of finding employment in a unionized or a nonunionized industry, respectively, if the offer of the manager contract is rejected. Applying the
19
As extensively discussed in Binmore, Rubinstein and Wolinksy (1986), the solution to the Nash bargaining
problem in (6) can be approximated by Rubinstein’s (1982) non-cooperative bargaining model with alternating
taking and leaving offers in which the bargaining parties differ in the time interval that elapses between one
party’s reaction to the other party’s offer and the own counter-offer. In such a setting, the party that needs more
time to formulate the own offer ends up with a lower bargaining surplus, which, in the labor economics literature,
is associated with a lower bargaining power of this party. Our approach can be interpreted as extension to this
reasoning, which captures the idea that the manager’s time for formulating a counter-offer depends on her effort
level.
8
implicit function theorem and noting that individual agents take economy-wide wages (𝑤 and
𝑤𝑐 ) as given, we get
𝑑𝑠 𝑑2 𝑠 𝑣 ′ (𝛾)
𝑣 ′′ (𝛾)𝜆𝑠 + 𝑣 ′ (𝛾)/𝑝2
and
=
,
(13)
=
𝑑𝛾 Γ=0
𝜆𝑠
𝑑𝛾 2 Γ=0
𝜆2𝑠
with
(
)
𝑠
1
𝑎−
.
(14)
𝜆𝑠 ≡
𝑝
𝑝
From (13), it follows that capital owners must offer a higher remuneration, in order to elicit
higher bargaining effort of the manager. Furthermore, provided that 𝑣 ′′ (𝛾) ≥ 0 holds, the
relationship between 𝑠 and 𝛾 turns out to be convex. This is the case, we are focussing on in the
subsequent analysis. In the interest of analytical tractability, we choose a simple specification
of 𝑣(𝛾) and parameterize disutility from managerial effort by 𝑣(𝛾) ≡ 𝑣1 𝛾, with 𝑣1 > 0.
The content of a manager contract, i.e. the (𝑠, 𝛾)-combination offered to the manager is
determined by a firm’s board of directors, which in general includes delegates of the group of
workers as well as the group of capital owners. Since the manager contract has no bearing on
the wage payment of workers if the labor market is competitive, in industries 𝑧 ∈ (¯
𝑧 , 1] no party
in the board of directors has an incentive to deviate from a contract with 𝛾 𝑐 = 0 and
√ (
)
(
)
𝑐
𝑠
𝑤 2
𝑤𝑐 2
= 𝑎 − 𝑧¯ 𝑎 −
+ (1 − 𝑧¯) 𝑎 −
,
(15)
𝑝
𝑝
𝑝
which fulfills the binding participation constraint in (12).20
In unionized industries, the worker’s delegate in the board of directors is the union leadership.
This delegate has the ovjective (𝑤𝑖 − 𝑤𝑐 )𝑞 𝑖 , which in view of our results in Subsection 3.2 equals
[(1−𝛾)/𝛾]𝜋. Intuitively, production workers are harmed by a 𝛾-increase, because a higher effort of
the manager reduces the share of rents accruing to them (without affecting firm output). Hence,
they would prefer the contract with the lowest possible effort level that still renders operating
the firm attractive from the capital owners’ perpsective. The capital owners’ objective equals
net profits: 𝑟 = 𝜋 − 𝑠 and, clearly, capital owners are only willing to participate in the bargain
if 𝑟 ≥ 0. An increase in 𝛾 exerts two counteracting effects on capital return 𝑟: it raises the
share of bargaining surplus accruing to the firm, but it also raises the salary for the manager.
This trade-off is illustrated in Fig. 1. In this figure, 𝜋(𝛾) denotes operating profits and 𝑠(𝛾) the
manager return as a function of effort 𝛾. These two expresssions are determined by (11) and
(12), respectively. Intuitively, if the disutility from managerial effort, 𝑣1 , is too large, a contract
that simulataneously fulfills both the participiation constraint of manager and the participation
constraint of capital owners does not exist. In this case, the board of directors fails to reach an
agreement and, hence, there is no production in unionized industries. This case is illustrated by
locus 𝑠(𝛾)∣𝑣1 =high . Since such an outcome is not of further interest, we focus on sufficiently small
𝑣1 -levels that allow for production in all sectors throughout the subsequent analysis. Then, two
scenarios can be distinguished. For intermediate levels of 𝑣1 , the 𝑟-maximizing contract leads to
an interior solution with 𝛾 < 1 (see locus 𝑠(𝛾)∣𝑣1 =medium ). In contrast, with disutility of effort
being sufficiently low, as illustrated by the 𝑠(𝛾)∣𝑣1 =low -locus, capital owners prefer a contract
with 𝛾 = 1. In order to facilitate our analysis, we focus on the latter scenario, in which capital
owners prefer a contract with 𝛾 = 1 and 𝑠(𝛾) = 𝑠(1) to any alternative on the 𝑠(𝛾)-locus.21 In
20
Notably, in non-unionized industries it is not entirely clear who serves as the worker’s delegate in the board of
directors, because the firm’s workforce is hired by the manager. For instance, one may assume that the worker’s
representative is ex ante assigned to the firm. Alternatively, one may as well assume that in non-unionized
industries the manager contract is unilaterally chosen by capital owners. In both of these cases, the preferred
manager contract would be given by 𝛾 𝑐 = 0 and (15).
21
Whether and how our results do change if we consider an intermediate level of 𝑣𝑖 is briefly discussed below.
9
this case, the conflict of interest between the two bargaining parties is most pronounced.
–Figure 1 about here–
Due to the exisitng conflict of interest between capital owners and workers, the concrete
specification of the manager contract depends on the relative strength of the two parties in the
board of directors decision process. We model this decision process by means of a Nash bargain
and bdenote by 𝜂 ∈ [0, 1] the bargaining power of the labor union and by 1 − 𝜂 the bargaining
power of capital owners, respectively. Then, the solution to the board’s bargaining problem can
be determined by maximizing the asymmetric Nash product
[
]𝜂
1−𝛾
𝐵(𝛾) =
𝜋(𝛾) [𝜋(𝛾) − 𝑠(𝛾)]1−𝜂 ,
(16)
𝛾
subject to the capital owners’s participation constraint 𝑟(𝛾) = 𝜋(𝛾) − 𝑠(𝛾) ≥ 0. This gives the
first order condition
[
]
𝐵 ′ (𝛾) = 𝜂 [𝜋(𝛾) − 𝑠(𝛾)] − (1 − 𝜂)(1 − 𝛾) 𝜋 ′ (𝛾) − 𝑠′ (𝛾) = 0,
(17)
which implicitly determines 𝛾 as a negative function of 𝜂. In view of our insights from Fig.
1, we can thus conclude that a larger influence of unions upon the board of director’s decision
leads to a lower manager remuneration and lower managerial effort in the wage-employment
negotiation with the union. This, however, just describes the partial equilibrium impact of 𝜂
on the manager contract, which has been derived under the assumption that 𝜂 changes only in
one industry. General equilibrium feedback effects that arise if 𝜂 changes simultaneously in all
unionized industries are addressed in the next subsection.
3.4
General equilibrium in the closed economy
With the above insights at hand, we can now proceed with determining the general equilibrium
outcome in the closed economy. For this purpose, we apply the labor market clearing condition,
which – in view of our finding that all firms have the same output level, irrespective of the
prevailing labor market regime – is given by
𝐿=
𝑁 (𝑎 − 𝑤𝑐 )
.
𝑏(𝑁 + 1)
(18)
Together with (8)-(16) this determines wages, salaries, employment, and profits in the autarky
equilibrium. The relative strength of labor unions and capital owners in the board of directors
does not affect competitive wage, 𝑤𝑐 , output level, 𝑞, and price level, 𝑝 – with 𝑝 = 𝑎 − 𝑏𝐿,
according to (10) and (18). Hence, a change in 𝜂 does not exert a direct effect on production
efficiency. However, by altering the contracted effort of managers, it affects welfare of the
represenatative consumer as well as utility of the different income groups. These consequences
are in the limelight of our interest next.
All other things equal, a stronger influence of workers on the board’s decision upon the
manager contract leads to a lower salary, 𝑠, and a lower effort, 𝛾, in unionized industries (see
above). The lower managerial effort in the wage-employment negotiation induces a higher union
wage premium, according to (8), so that the expected utility of production workers goes up,
thereby rendering workers in general (and those in unionized industries in particular) better off
after the increase in 𝜂. Crucially, the surge in the union wage rate exerts a feedback effect on
salaries and managerial effort. By raising expected utility outside the contract, an increase in
𝜂 stimulates manager remuneration in non-unionized industries (see Eq. (15)) and, at the same
10
time, increases the compensation that is necessary to elicit a given level of managerial effort in the
wage-employment negotation with unions. Graphically, this is captured by an upward shift of the
𝑠(𝛾) locus in Fig. 1 and thus induces a fall in the contracted 𝛾-level. However, this second-round
effect is not strong enough to reverse the positive (partial equilibrium) impact effect, so that 𝛾
unambiguously falls in response to an increase in 𝜂. With total output staying constant, this
implies that welfare of the representative consumer goes up if the relative bargaining power in the
board of diretors shifts towards workers (see Eq. (1)). The decline in 𝛾 lowers the compensation
of managers in unionized industries relative to managers in non-unionized industries. As a
consequence, 𝑠(𝛾) may rise or fall in response to an increase in 𝜂. Intuitively, if the share of
unionized sectors is sufficiently low, the increase in the union wage premium does not alter the
outside income opportunities of managers significantly and 𝑠𝑐 remains more or less unaffected.
In this case, the decline in 𝛾 is relatively large and 𝑠(𝛾) will fall if workers get a stronger influence
on the board of director’s decision upon the manager contract. Despite the possibly negative
impact of an increase in 𝜂 on manager remuneration in unionized industries, it is nonetheless
clear that all managers must be better off after the increase in 𝜂. The reason is that utility levels
of managers in unionized and non-unionized industries are linked by the participation constraint
in (12), so that the salary rise in non-unionized industries is sufficient for an overall increase in
manager welfare.
Finally, changes in 𝜂 also exert an impact on the welfare of capital owners. On the one hand,
an increase in 𝜂 lowers net profits in unionized industries. This is intuitive, as a higher 𝜂 implies
that managers provide lower bargaining effort, so that unions can acquire a larger share of the
bargaining surplus in the wage-employment nergotiation with the firm. This lowers welfare of
capital owners. Furthermore, as has been noted above, the higher wage income of production
workers raises expected utility of managers outside the contract and thus increases manager
remuneration in non-unionized industries, 𝑠𝑐 . This reinforces the first effect and, hence, income
and welfare of capital owners unambiguously fall if 𝜂 increases.
We complete our discussion regarding the impact of changes in 𝜂 on welfare of the representative consumer as well as memebers the different income groups by summarizing the main
insights from above in the following proposition.
Proposition 1. A stronger influence of workers in the board of directors lowers managerial
effort in the wage bargain. This raises welfare of the representative consumer and shifts income
from capital owners to workers, who unambiguously benefit. The wage increase, on the other
hand, improves the managers’ expected utility outside the contract and thus raises the welfare
level of this group of agents. Only capital owners lose from stronger representation of workers
in the board of directors.
With these insights at hand, we can now apply our model for analyzing to what extent local
corporate governance insitutions and their interaction with labor market imperfections determine
welfare of the representative consumer as well as the well-being of different income groups.
Thereby, we look at two polar cases of corporate governance institutions, which we associate
with the US and Europe, respectively. Since in the US, workers do not have a legal right to
participate in the board of directors, we represent US firms by the limiting case 𝜂 = 0. This
implies a manager contract with 𝛾 → 1 and 𝑠 = 𝑠(1) in unionized industries. As a consequence,
unions lose their impact on wage setting and the union wage premium vanishes: 𝑤 = 𝑤𝑐 ,
according to (8). Furthermore, 𝑠𝑐 = 𝑤𝑐 , and
√
(
)
𝑠(1)
𝑤𝑐 2
= 𝑎 − 2𝑣1 + 𝑎 −
.
(19)
𝑝
𝑝
11
With 𝑤𝑐 being determined according to (18), it is then immediate that deunionization, which
is captured by a decline in 𝑧¯, does not exert an impact on real factor returns at the intensive
margin, i.e. in industries that keep their status of unionization. However, there are effects at
the extensive margin, since managers in newly deunionized industries reduce their bargaining
effort and lose income. The decline in aggregate bargaining effort generates welfare gains for
the representative consumer, according to (1). Furthermore, the fall in manager remuneration
in these industries affects both managers and capital owners. While managers are compensated
for their income loss by a utility gain due to lower effort costs and thus do not experience a
welfare change, capital owners receive higher income and hence are better off after the decline
in 𝑧¯. In summary, we can thus conclude that in the case of US firms there is no income group
that is better off with a higher degree of unionization, which offers a reasoning for the empirical
observation that both union density and coverage are relatively small in the US economy.
In Europe, employees have a legal right to participate in the board of directors and often
possess quasi-veto power in its decision process. We therefore represent European firms by the
limiting case of 𝜂 = 1, impliyng that labor unions can unilaterally determine the content of the
manager contract in industries 𝑧 ∈ [0, 𝑧¯] and thus choose a contract with 𝛾 = 𝛾ˆ and 𝑠 = 𝑠(ˆ
𝛾 ),
where effort level 𝛾ˆ is implicitly determined by the participation constraints of managers and
capital owners. The former one is given by (12) and the latter one represented by 𝜋(ˆ
𝛾 ) = 𝑠(ˆ
𝛾 ).
Putting these two constraints together, we obtain Γ(𝜋(ˆ
𝛾 ), 𝛾ˆ ) = 0. Applying the implicit function
theorem, gives 𝑑ˆ
𝛾 /𝑑¯
𝑧 > 0, so that deunionization in Europe lowers managerial effort in the wageemployment negotiations of unionized industries. This has non-trivial consequences for wages:
Workers in non-unionized industries are unaffected by the decline in 𝑧¯, while those who are
employed in industries that are newly deunionized lose. Finally, workers who are employed in
industries that remain unionized benefit from lower managerial effort in the wage-employment
bargain. This implies that in Europe the union wage premium unambiguously increases in
response to deunionization, while the impact on the the average wage income is not clearcut in
general. For low levels of 𝑧¯ the number of workers employed in unionized industries is small and,
hence, only few agents can benefit from the higher union wage premium, so that the average
wage may fall when 𝑧¯ decreases. On the contrary, if the share of unionized sectors is large, a
large proportion of workers benefits from a higher union wage premium, so that in this case
the average wage may actually increase if 𝑧¯ declines. While the change in the average wage
income is not clearcut in general, the expected utility of production workers definitely decreases
in response to deunionization. This is formally shown in the appendix.
Regarding the impact of deunionization on manager remuneration 𝑠, we find that the lower
level of contracted effort induces a reduction of the manager return in unionized industries,
𝑠(ˆ
𝛾 ). This effect is reinforced by a decline in the expected income outside the contract (see
above), which lowers the return to managers in non-unionized industries, 𝑠𝑐 , and corresponds
to a downward shift in the 𝑠(𝛾)-locus in Fig. 1. Since manager utility in all sectors is linked by
indifference condition (12), we can thus safely conclude that all managers must be worse off with
a lower share of unionized industries. Finally, with net profits being equal to zero in unionized
sectors, capital owners definititely benefit from additional profit income in newly deunionized
industries. Beyond that, they also benefit from lower manager remuneration in industries that
have already been non-unionized prior to the decline in 𝑧¯. Taking stock, our analysis indicates
that deunionization, even though offering welfare gains for the representative consumer due to
lower managerial effort, is much more controversial in Europe than in the US, which offers an
explanation for the relatively high degrees in union density and coverage in continental European
labor markets.
We complete our discussion of the closed economy with a brief summary of the most important insights regarding the effects of deunionization on workers, managers and capital owners.
12
Proposition 2. In the US, deunionization lowers total managerial effort and stimulates welfare
of capital owners as well as the representative consumer, while welfare of workers and managers
remains unaffected. In Europe, the effects of deunionization on total managerial effort, the
welfare of capital owners and the welfare of the representative consumer are qualitatively the
same as in the US. However, managers as well as workers in newly deunionized industries lose,
while workers in unionized industries benefit from a decline in 𝑧¯.
4
Governance and trade
In this section, we investigate how a movement from autarky to free trade affects labor market
outcome and the manager contracts. Thereby, we assume that the countries that are involved in
international trade are identical in all respects, except of the prevailing governance institutions.
In this case, opening up to trade exerts a pro-competitive effect without changing aggregate
output and prices (similar to a featureless economy in Neary, 2009). However, trade affects the
distribution of economic rents in our model, and we are in particular interested how and to
what extent these distributional consequences depend on the prevailing corporate governance
institutions.
Since the trade effects in our model are monotonic in the number of trading partners, we
can set the number of countries that exchange products in international markets equal to 𝑘 ≥ 1,
with 𝑘 = 1 referring to the autarky scenario. With these insights at hand, we can now proceed in
analogy to Section 3 in order to determine the partial equilibrium outcome in the open economy.
This gives
𝑎 − 𝑤𝑐
𝑤 = 𝑤𝑐 + (1 − 𝛾)
,
(8′ )
𝑘𝑁 + 1
𝑞=
𝑘(𝑎 − 𝑤𝑐 )
,
𝑏(𝑘𝑁 + 1)
𝑎 + 𝑘𝑁 𝑤𝑐
,
𝑘𝑁 + 1
(
)
𝛾𝑘 (𝑎 − 𝑤𝑐 ) 2
𝜋=
,
𝑏
𝑘𝑁 + 1
𝑝=
(9′ )
(10′ )
(11′ )
with (8′ )-(11′ ) reducing to the autarky expressions in (8)-(11) if 𝑘 = 1. Furthermore, the general
equilibrium outcome in the open economy can be determined by additionally accounting for the
labor market clearing condition
𝑘𝑁 (𝑎 − 𝑤𝑐 )
𝐿=
.
(15′ )
𝑏(𝑘𝑁 + 1)
Together, Eqs. (12), (8′ )-(15′ ), and the solution to the bargaining problem in (17) characterize
the free trade equilibrium in our model.
A detailed comparison of the trade equilibrium with the respective autarky equilibrium is
at the agenda of the next two subsections. In Subsection 4.1, we start with discussing the
consequences in countries with capital owner dominace in the board of directors (𝜂 = 0), as
it is the case in US firms. In Subsection 4.2 we then address the case of worker dominance in
the board of directors (𝜂 = 1), which represents corporate governance institutions in European
firms.
13
4.1
Corporate governance institutions with capital owner dominance
Similar to Neary (2009), the opening up to trade stimulates aggregate labor demand, due to a
pro-competitive effect in goods markets which provides an incentive for firms (and unions) to
expand production. With an exogenous labor endowment, this drives up the competitive wage
until the excess demand for labor falls to zero. This stimulus for the competitive wage can be
seen from differentiating (15′ ) with respect to 𝑘. This gives
𝑑𝑤𝑐
𝑏𝐿
= 2 > 0.
𝑑𝑘
𝑘 𝑁
(20)
From (20) we can deduce that the impact of trade on the competitive wage does not depend on
the prevailing corporate goevernance institutions. And, all other things equal, the increase in
𝑤𝑐 improves the outside income opportunities of managers, so that firms in unionized industries
have to offer a higher salary in order to elicit a given level of effort by managers in the wage
employment negotiations with unions (see(12)). This induces an upward shift of the 𝑠(𝛾)-locus
as illustrated in Fig. 2. Furthermore, the pro-competitive effect in the goods market lowers
firm profits for any given level of managerial effort and thus induces a clockwise rotation of
the 𝜋(𝛾)-locus. As long as the rotation and shift effects in Fig. 2 are not too pronounced, the
preferred contract of capital owners remains to be characterized by the corner solution 𝛾 = 1
and 𝑠(𝛾) = 𝑠(1) in the open economy. In this case, we have 𝑤 = 𝑤𝑐 as in the closed economy, so
that the increase in the competitive wage induces a pari passu increase in the union wage. This
triggers a second round shift in 𝑠(𝛾)-locus in Fig. 2 and thus implies the manager remuneration
unambiguously increases in both unionized and non-unionized industries. Hence, we can safely
conclude that workers as well as managers are better off in the open economy if capital owners are
the dominant decision makers in the board of directors. However, while factor returns increase
after the opening up to trade, there is no stimulus on aggregate output, so that, similar to
Neary’s (2009) featureless economy, welfare stays constant if capital owners stick to the contract
𝛾 = 1, 𝑠(𝛾) = 𝑠(1) in the open economy. However, with a constant utility of the representative
consumer and higher utility of workers and managers, it is immediate that capital owners must
be worse off after the fall in trade barriers, due to a decline in their profit income.
–Figure 2 about here–
The above results have been derived under the assumption that capital owners stick to the
contract with 𝛾 = 1, 𝑠(𝛾) = 𝑠(1) in the open economy. However, this needs not be the case. If
the rotation and shift effects analyzed above are sufficiently pronounced, it may well be the case
that capital owners benefit from reducing the contracted manager effort. This case is illustrated
in Fig. 3. We can see from this figure that the capital return maximizing contract is characterized
by the two conditions 𝑠′ (𝛾) = 𝜋 ′ (𝛾) and (12), and the unionized firm offers a manager contract
with 𝛾 < 1 and 𝑠(𝛾) < 𝑠(1) in this case. The 𝛾-reduction implies that managers reduce their
effort in the wage-employment negotiations, so that in the open economy union members get a
wage premium even if capital owners unilaterally determine the manager contract. This provides
a second-round positive wage effect, thereby further improving the outside option of managers
and thus raising this groups’ remuneration in non-unionized industries. Regarding manager
remuneration in unionized industries, we can identify two opposing effects. While similar to
non-unionized industries, manager remuneration increases with ceteris paribus increase with the
outside income opportunities, there is a counteracting effect from a decline in the contracted
effort level. Irrespective of which of these two effects dominates, we can still conclude that all
managers must be better of in the open economy, because utility of managers in unionized industries is linked to utility of managers in non-unionized industries by the participation constraint
14
in (12). With respect to the income of capital owners, we can note that the 𝛾-reduction itself
raises the return to this group of agents. However, this indirect effect cannot offset the direct
negative effect for a given 𝛾. To see this, note that firms in non-unionized industries pay higher
wages and manager remuneration, so that profit income in this sectors unambiguously falls,
when taking into account that output stays constant in all firms and industries. In unionized
industries, it has not been shown that manager remuneration increases along with wages and,
hence, we cannot exclude that factor costs shrink in these industries. However, we can read off
Fig. 3 that 𝐴𝐵 < 𝐶𝐷, while 𝐶𝐷 < 𝜋𝑎 (1) − 𝑠𝑎 (1) (with subscript 𝑎 referring to autarky), so that
profit income in unionized sectors definitely shrinks when a country opens up for trade. Hence,
we can safely conclude that, irresepective of whether the contracted 𝛾 stays constant or not, an
opening up for trade definitely redistributes income from capital owners to production workers
and managers. However, with a falling 𝛾 there are now aggregate gains from trade, because less
effort is wasted for rent extraction of capital owners.
–Figure 3 about here–
The main insights from the above analysis are summarized in the following proposition.
Proposition 3. If the board of directors is dominated by capital owners, a country’s openeing
up to trade redistributes income from capital owners to production workers and managers. Furthermore, there are aggregate gains form trade only if the contracted effort level of managers falls
in respose to trade, so that less effort is wasted for rent extraction of capital owners. Otherwise,
trade does not exert efficiency effects, despite existing differences across sectors in the prevailing
labor market institutions.
4.2
Coporate governance institutions with worker dominance
The impact of trade on the competitive wage does not depend on corporate government institutions, so that 𝑤𝑐 unambiguously increases when a country opens up for trade, according to
(20). As noted above, this improves outside income opportunities of managers and thus induces
a first-round shift in the 𝑠(𝛾)-locus similar to Fig. 2. Furthermore, the pro-competitive effects
in the product market induces a clockwise rotation of the 𝜋(𝛾)- locus and, hence, there is a
presumption from looking at Fig. 2 that managerial effort, which is now determined by the two
conditions 𝑠(𝛾) = 𝜋(𝛾) and (12), is higher in the open than in the closed economy. However, a
higher 𝛾, ceteris paribus implies a fall in the union wage, with counteracting effects on manager
remuneration and the contracted effort level. As formally shown in the appendix, this counteracting effect is of second order, regarding its impact on manager effort and, hence, we obtain
𝑑ˆ
𝛾 /𝑑𝑘 > 0. However, we can also show that increase in 𝛾 induces a fall in the union wage,
𝑑𝑤/𝑑𝑘, so that workers are asymmetrically affected by trade if workers unilaterally determined
the conditions of the manager contract. Indeed, similar to other studies on the matter unions
have a lower scope for extracting rents in an open economy and thus the union wage premium
falls in response to trade.
With wages in unionized and non-unionized industries going into opposite directions, it is
in general not clear whether the outside income opportunities of managers improve or worsen.
Intuitively, these income opportunities will improve if the probability of finding a job in a nonunionized sector is sufficiently high, i.e. if 𝑧¯ is not too large. In this case, manager remuneration
in non-unionized industries goes up, according to (15), and so does manager remuneration in
unionized sectors because the increase in 𝛾 reinforces the positive impact of a higher outside income opportunity on 𝑠(𝛾). Hence, managers unambiguously benefit from a country’s movement
15
to trade if 𝑧¯ is not too large. On the contrary, if the share of unionized sectors is sufficiently high,
the second-round fall in union wages dominates the first-roun increase in the competitive wage,
thereby lowering outside income opportunities of managers. In this case, managers are worse off
in the open than in the closed economy. Regarding the income of capital owners, we can note
that profit income in unionized industries falls to zero if workers can unilaterally decide upon the
manager contract. Hence, capital income is determined by profits in non-unionized industries
and these profits definitely fall if 𝑧¯ is not too large, as both wages and manager remuneration
increase in this case (see above). However, even if manager remuneration falls, capital income
is likely to decrease because of the stimulus in 𝑤𝑐 . But an outcome with 𝑑𝜋 𝑐 /𝑑𝑘 > 0 cannot
be ruled out in general if 𝑧¯ is close to one. Finally, trade generates aggregate losses if 𝜂 = 1,
because more effort is wasted for rent extraction of capital owners in the open economy.
The main insights from the above analysis are summarized in the following proposition.
Proposition 4. If the board of directors is dominated by workers, a country’s opening up to
trade redistributes redistributes income from capital owners to production workers and managers,
provided that the share of unionized industries is not too high. However, not all workers equally
share in this groups’ gains from trade. While workers in non-unionized industries are better off in
the open economy, workers in unionized sectors lose from a fall in trade barriers. Furthermore,
there are aggregate losses form trade since more effort is wasted for rent extraction of capital
owners in an open economy.
5
Conclusion: Wild Speculation
16
Appendix
The impact of 𝜂 on manager remuneration and effort
Starting point is Eq. (17), which determines the solution to the Nash-bargaining problem in
the board of directors and thus the 𝐵-maximizing 𝛾 level as a function of 𝜂. Clearly, in our
model firms rationally ignore their impact on aggregate variables and, hence, treat outside wages
parametrically. However, in the general equilibrium, these wages themselves are endogenous and
a par passu increase of 𝛾 in all unionized industries exerts a negative impact on the unionized
wage rate:22
𝑑𝑤
𝑏𝐿
=−
< 0.
(21)
𝑑𝛾
𝑁
This change in 𝑤 exerts a negative feedback effect on manager remuneration in all industries,
which we have to account for in the subsequent analysis. To avoid clutter, we introduce a
new variable 𝑠ˆ(𝛾), which is implicitly determined by (12), when accounting for the endogenous
adjustment of 𝑤, according to (21). Totally differentiating Γ and setting the resulting expression
equal to zero, we obtain
𝑑ˆ
𝑠
𝜆𝑤 𝑏𝐿
𝑣1
− 𝑧¯
=
,
(22)
𝑑𝛾
𝜆𝑠
𝜆𝑠 𝑁
where 𝜆𝑤 is defined in analogy to 𝜆𝑠 , with 𝑤 assuming the role of 𝑠. With these insights at
hand, we can rewrite first-order condition 𝐵 ′ (𝛾) = 0 as follows:
[
]
Ω(𝜂, 𝛾) ≡ 𝜂 [𝜋(𝛾) − 𝑠ˆ(𝛾)] − (1 − 𝜂)(1 − 𝛾) 𝜋 ′ (𝛾) − 𝑠′ (𝛾) = 0,
(23)
where, 𝜋(𝛾), 𝜋 ′ (𝛾) and 𝑠′ (𝛾) = 𝑣1 /𝜆𝑠 are independent of 𝑤. Then, applying the implicit function
theorem and noting that 𝜋 ′′ (𝛾) = 0 , according to (11) and (18), we obtain
𝜋(𝛾) − 𝑠ˆ(𝛾) + (1 − 𝛾) [𝜋 ′ (𝛾) − 𝑠′ (𝛾)]
𝑑𝛾
=−
.
𝑑𝜂
𝜂 [𝜋 ′ (𝛾) − 𝑠ˆ′ (𝛾)] + (1 − 𝜂) [𝜋 ′ (𝛾) − 𝑠′ (𝛾)] + (1 − 𝜂)(1 − 𝛾)𝑠′′ (𝛾)
(24)
Furthermore, noting that 𝜋(𝛾) ≥ 𝑠(𝛾) must hold due to the participation constraint of managers
and accounting for 𝜋 ′ (𝛾) > 𝑠′ (𝛾) > 𝑠ˆ′ (𝛾) (see Fig. 1 and Eqs. (13), (22)), and 𝑠′′ (𝛾) = 𝑣1 /[𝑝2 𝜆2𝑠 ] >
0, we can safely conclude that 𝑑𝛾/𝑑𝜂 < 0 still holds, if we account for the general equilibrium
feedback effect through adjustments in 𝑤.
The impact of deunionization on wages, salary, and welfare of workers and
managers if 𝜂 = 1
Substituting 𝜋(𝛾) = 𝑠(𝛾) in (12) and applying the implicit function theorem, gives
𝑑ˆ
𝛾
1 [𝜆𝑤 + 𝜆𝑤𝑐 ] (1 − 𝛾ˆ )𝑏𝐿/𝑁
=
,
𝑑¯
𝑧
2 𝑧¯𝜆𝑤 𝑏𝐿/𝑁 + 𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1
(25)
which is positive, as 𝜋 ′ (𝛾) > 𝑣1 /𝜆𝑠 holds at 𝛾 = 𝛾ˆ (see Fig. 1). Using the latter in 𝑑𝑤/𝑑¯
𝑧 =
𝑑𝑤/𝑑𝛾 × 𝑑ˆ
𝛾 /𝑑𝑧, further implies
𝑑𝑤
1 [𝜆𝑤 + 𝜆𝑤𝑐 ] (1 − 𝛾ˆ )𝑏𝐿/𝑁 𝑏𝐿
=−
,
𝑑¯
𝑧
2 𝑧¯𝜆𝑤 𝑏𝐿/𝑁 + 𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1 𝑁
22
(26)
By virtue of (18), we have 𝑏𝐿/𝑁 = (𝑎 − 𝑤𝑐 )/(𝑁 + 1). Substituting the latter together with 𝛽 = 𝛾/(1 − 𝛾)
into (8), we obtain 𝑤 = 𝑤𝑐 + (1 − 𝛾)𝑏𝐿/𝑁 . Diferentiating 𝑤 with respect to 𝛾, finally gives (21)
17
so that the wage rate in unionized industries shrinks, if 𝑧¯ increases. On the other hand, workers
in newly unionized industries experience a wage increase, implying that the total impact of an
increase in 𝑧¯ on the average wage of production workers, 𝑤,
˜ is given by
𝑑𝑤
˜
2 [𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1 ] + 𝑧¯ [𝜆𝑤 − 𝜆𝑤𝑐 ] 𝑏𝐿/𝑁 (1 − 𝛾ˆ )𝑏𝐿
=
.
𝑑¯
𝑧
2 [¯
𝑧 𝜆𝑤 + 𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1 ]
𝑁
(27)
Noting that 𝜆𝑤 − 𝜆𝑤𝑐 = −(1 − 𝛾ˆ )𝑏𝐿/(𝑝𝑁 ) < 0, it is immediate that 𝑑𝑤/𝑑¯
˜ 𝑧 > 0 is guaranteed
for sufficiently small levels of 𝑧¯, while the sign of 𝑑𝑤/𝑑¯
˜ 𝑧 is not clearcut for arbitrary levels of
𝑧¯.23 However, this does not imply that an increase in 𝑧¯ exerts an ambiguous impact on expected
utility of workers and thus on utility of managers in non-unionized industries. Differentiating
Eq. (15) with respect to 𝑧¯ implies that
𝑑𝑠𝑐
𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1
(1 − 𝛾ˆ )𝑏𝐿
𝜆𝑤 + 𝜆𝑤 𝑐
=
,
𝑑𝑝
2𝜆𝑠𝑐
𝑧¯𝜆𝑤 𝑏𝐿/𝑁 + 𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1
𝑁
(28)
which is unambiguously positive. Hence, managers in non-unionized industries are definitely
better off if 𝑧¯ increases, which in view of (12) and (15) implies that expected utility of production
workers must be stimualted if the degree of unionization goes up.
Trade effects in the case of worker dominance in the board of directors
First of all, we study the impact of an increase in 𝑘 on 𝛾 and 𝑠. For this purpose, we substitute
𝑠(𝛾) = 𝜋(𝛾) into (12), totally differentiate the resulting expression with respect to 𝑘 and setting
the first derivative equal to zero. This gives:
𝑑ˆ
𝛾
𝑏𝐿 𝑧¯𝛾ˆ 𝜆𝑤 + (1 − 𝑧¯)𝜆𝑤𝑐 + 𝜆𝑠 𝛾ˆ 𝐿/𝑁
= 2
> 0.
𝑑𝑘
𝑘 𝑁 𝑧¯𝜆𝑤 𝑏𝐿/(𝑘𝑁 ) + 𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1
(29)
𝑑𝑤
𝑑𝑤𝑐
𝑏𝐿 𝑑ˆ
𝛾
𝑏𝐿
=
−
− (1 − 𝛾)
,
𝑑𝑘
𝑑𝑘
𝑘𝑁 𝑑𝑘
𝑘𝑁
(30)
Noting further that
it follows from (20) and (29) that
[
]
𝑑𝑤
𝑏𝐿 𝛾ˆ 𝑑ˆ
𝛾
=
−
𝑑𝑘
𝑘𝑁 𝑘 𝑑𝑘
𝛾)
𝑏𝐿 (1 − 𝑧¯)𝜆𝑤𝑐 𝑏𝐿/(𝑘𝑁 ) + 𝑣(ˆ
=− 2
< 0.
′
𝑘 𝑁 𝑧¯𝜆𝑤 𝑏𝐿/(𝑘𝑁 ) + 𝜆𝑠 𝜋 (ˆ
𝛾 ) − 𝑣1
(31)
Regarding the impact of an increase in 𝑘 on 𝑠𝑐 , we can totally differentiate
[ (
)2
(
) ]
(
)
𝑐 2
1
𝑤
𝑤
1
𝑠𝑐 2
𝑐
Γ ≡
𝑧¯ 𝑎 −
+ (1 − 𝑧¯) 𝑎 −
−
𝑎−
2
𝑝
𝑝
2
𝑝
and set the resulting expression equal to zero. This gives
[
]
𝑑𝑠𝑐
1
𝑏𝐿
𝑏𝐿 𝑑ˆ
𝛾
𝑐
=
(¯
𝑧
𝛾
ˆ
𝜆
+
(1
−
𝑧
¯
)𝜆
)
−
𝑧
¯
𝜆
.
𝑤
𝑤
𝑤
𝑑𝑘
𝜆 𝑠𝑐 𝑘 2 𝑁
𝑘𝑁 𝑑𝑘
23
(32)
The ambiguity in the sign of 𝑑𝑤/𝑑¯
˜ 𝑧 for arbitrary levels of 𝑧¯ has been confirmed in a simulation exercise, with
the respective program code for Mathematica 6.0 being available upon request.
18
Then, noting that
𝑑Γ
=0
𝑑𝑘
⇐⇒
) 𝑑ˆ
𝛾 (
𝑏𝐿
𝑏𝐿 𝑑ˆ
𝛾
𝜋(ˆ
𝛾)
(¯
𝑧 𝛾ˆ 𝜆𝑤 + (1 − 𝑧¯)𝜆𝑤𝑐 ) − 𝑧¯𝜆𝑤
= 𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1
− 𝜆𝑠
2
𝑘 𝑁
𝑘𝑁 𝑑𝑘
𝑑𝑘
𝑘
holds, according ot (12), we get write
[
]
) 𝑑ˆ
𝜋(ˆ
𝛾)
𝑑𝑠𝑐
1 (
𝛾
′
𝜆𝑠 𝜋 (ˆ
𝛾 ) − 𝑣1
,
=
− 𝜆𝑠
𝑑𝑘
𝜆 𝑠𝑐
𝑑𝑘
𝑘
which after tedious but straighforward calculations can be further simplified to
𝑑𝑠𝑐
𝛾 )(1 − 𝑧¯)𝜆𝑤𝑐 − 𝑣1 [¯
𝑧 𝛾ˆ 𝜆𝑤 + (1 − 𝑧¯)𝜆𝑤𝑐 ]
1 𝑏𝐿 𝜆𝑠 𝜋 ′ (ˆ
,
=
2
𝑑𝑘
𝜆𝑠𝑐 𝑘 𝑁
𝑧¯𝜆𝑤 𝑏𝐿/(𝑘𝑁 ) + 𝜆𝑠 𝜋 ′ (ˆ
𝛾 ) − 𝑣1
(33)
which can shown to be positive if 𝑧¯ is small, while 𝑑𝑠𝑐 /𝑑𝑘 < 0 if 𝑧¯ → 1.
To determine the impact of an increase in 𝑘 on 𝑠(ˆ
𝛾 ), we can not that 𝑑𝑠(ˆ
𝛾 )/𝑑𝑘 = 𝑑𝜋(ˆ
𝛾 )/𝑑𝑘
and thus
[
]
𝑑𝑠(ˆ
𝛾)
𝑑ˆ
𝛾 𝛾ˆ
′
= 𝜋 (ˆ
𝛾)
−
,
(34)
𝑑𝑘
𝑑𝑘 𝑘
which in view of (31) is unambiguously positive. Finally, differentiating 𝑟𝑐 = 𝜋 𝑐 −𝑠𝑐 with respect
to 𝑘, we obtain
𝜋 𝑐 𝑑𝑠𝑐
𝑑𝑟𝑐
=− −
.
𝑑𝑘
𝑘
𝑑𝑘
(35)
Hence, 𝑑𝑟𝑐 /𝑑𝑘 < 0 is guaranteed if 𝑧¯ is not too large, while we are not able to rule out 𝑑𝑟𝑐 /𝑑𝑘 > 0
if 𝑧¯ → 1.
19
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