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HB31
.M415
working paper
department
of economics
THE MACROECONOMICS OF SPECIFICITY
Ricardo
J.
Caballero
Mohamad L. Hainmour
96-25
September, 1996
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
THE MACROECONOMICS OF SPECIFICITY
Ricardo
J.
Mohamad
96-25
Caballero
L.
Hammour
September, 1996
—
iV,/.3ii.'-.::.j::l,:J
p.
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-
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The Macroeconomics
Ricaxdo
J.
of Specificity
Mohamad
Caballero
August
31,
L.
Hammour*
1996
Abstract
Specific quasi-rents build
posed to opportunism unless
up
a wide variety of economic relationships, and are ex-
in
fully protected
tracts are often incomplete has yielded
by contract. The recognition that such con-
major
insights into the organization of microe-
conomic exchange. Rent appropriation, we argue, also
impUcations.
suffers
hsis
important macroeconomic
Resources are underutilized, factor markets are segmented, production
from technological
"sclerosis,"
recessions are excessively sharp,
job destruction
is
out of balance with creation,
and expansions run into bottlenecks. While, depending
on the nature of the shock, expansions may require reinforcement or
sions should always
be softened. In the long run,
capital-labor relations,
may
stabilization, reces-
institutions, such as those governing
evolve to alleviate the problem by balancing appropriation.
Technology choice will also be
affected,
with the appropriated factor partially "exclud-
ing" the other from production to reduce appropriation
capital-labor substitution played in the rise of
—
as manifested in the role
European unemployment.
Introduction
1
An
asset
specific to a relationship to the extent that its value
is
relationship than outside.
Economic
specificity
is
is
greater within the
a pervasive phenomenon.
It arises
when
a firm selects and invests in a worker; when the worker spends his learning years in a firm;
when
capital
entrepreneur;
when
is
invested in a unionized firm or industry;
when an upstream
firm
makes investments
to serve
credit to
an
downstream customers;
foreign direct investment flows into a country.
'Respectively:
MIT and NBER;
Capital Guidance.
and the
NBER
financial support.
1996
Summer
Institute
We
are grateful to Giuseppe Bertola, Olivier Blan-
ECARE, LSE, IMF, MIT, NYU, OFCE, Wharton,
(EFCCL) for helpful comments. Caballero thanks the NSF for
chard, Peter Diamond, and seminar participants at
Yale,
when a bank extends
Specificity in a relationship reduces the flexibihty of separation decisions,
reluctance in the investment decision. This
ment
But
literature.
the basic insight of the irreversible invest-
specificity acquires a potentially
combined with contracting
difficulties.
more troublesome dimension when
To the extent that
relationship creates specific quasi-rents that
parties' ex ante
is
which induces
may
it is
irreversible, entering into a
not be divided ex post according to the
terms of trade. Avoiding this transformation from an ex ante competitive
— known in the
as the "fundamental
transformation" or the "holdup problem" — requires prior protection through comprehen-
situation to an ex post bilateral
sive
monopoly
literature
and enforceable long-term contracts. The problem
closer to a methodological
is
that such contracts are
benchmark than a description of actual
much
practices.^
Relationship specificity, together with the recognition of the difficulties involved in actual contracting,
(Klein,
is
a central building block in the modern economic theory of institutions
Crawford and Alchian 1978; Williamson 1979 and 1985). Specificity as a central
dimension of transaction description forms the basis of insightful theories of the firm and
internal organization (e.g.,
cial
structure
(e.g.,
Grossman and Hart
1986; Hart
and Moore 1990), of
Williamson 1988; Hart and Moore 1994; Shleifer and Vishny 1995),
of public-choice institutions and credibility
(e.g..
North and Weingast 1989; Thomas and
Worrall 1994), and a variety of other institutional arrangements. The
those theories
is
finan-
common
the idea that a main function of institutional arrangements
is
feature in
to allow the
transacting parties to partly circumvent the holdup problem.
The
institutional literature generally acknowledges that, while institutions often help
alleviate appropriability, they rarely resolve the
problem
spective, the prevalence of unprotected specific rents
fully.
makes
it
From a macroeconomic
per-
a potentially central factor in
determining the functioning of the aggregate economy. Transactions in the labor, capital.
^The problem
of the appropriability of relationship-specific investment goes back early in the history
Marx, in Das Capital, saw in it a channel for the capitaUst exploitation of labor:
"The knowledge, the judgement, and the will, which, though in ever so small degree, are practiced by the
independent peasant or handicraftsman [...]
these faculties are now required only for the workshop as a
whole. Intelligence in production expands in one direction, because it vanishes in many others. What is lost
by the detail laborers, is concentrated in the capital that employs them [...]" {as cited by Rosenberg 1965).
Simons (1944) took the opposite view, that it is labor that takes advantage of specificity to approriate
capital; "Frankly, I can see no reason why strongly organized workers, in an industry where huge investment
is already sunk in highly durable assets, should ever permit a return on investment sufficient to attract
of economic thought.
—
new
capital or even to induce full maintenance of existing capital."
resulting under-investment: "[t]he bias against
[...].
[...].
new investment
He provided an
early analysis of the
inherent in labor organization
is
important
the prospect that labor organizations will appropriate most or aU of the earnings
Indeed, every new, long-term commitment of capital is now a matter of giving hostages to organized
Investors
sellers of
now
face
[...]
complementary
services."
or goods markets axe frequently characterized by some degree of specificity.
a job,
for
worker
The
creation of
example, typically involves relationship-specific investments by the firm and the
(e.g.,
Becker 1964). Beyond
be increased by such
option of using
its
its
purely technological aspect, effective specificity
may
institutional features as dismissal regulations (which devalue the firm's
investment outside the relationship) or unionization (which narrows the
firm's outside option to a sector outside the scope of the union). In partial equilibrium, un-
resolved opportunism results in reduced investment incentives, because the resulting specific
quasi-rents
may
later
be partly appropriated by others
(e.g.,
Simons 1944; Grout 1984). In
general equilibrium, as the problem of creating and sharing quasi-rents spreads throughout
the economy, the market system will adjust to help compensate the appropriated factors,
providing a highly inefficient macroeconomic "solution" to the unresolved microeconomic
contracting problems. This general-equilibrium adjustment can affect major aspects of the
aggregate functioning of the economy.
In this paper
nomic "solution"
we attempt
to characterize the nature
to the holdup problem.^
and implications of the macroeco-
Throughout the paper we think of the problem
one where two factors of production contemplate either committing to a partly
as
irreversible
joint-production relationship, or remaining in "autarky." Section 2 sets up this model and
draws some basic macroeconomic implications. The problem of appropriabihty
im.plies, in
general equilibrium, that factors of production are underemployed; that the market for the
"appropriating" factor
is
segmented
(i.e., it
production); that the productive structure
units axe kept in operation
economy
ation.
compared to an
experiences involuntary unemployment in joint
is
"sclerotic"
efficient
(i.e.,
too
low-productivity
economy); and that, paradoxically, the
exhibits excessive destruction of production units given
The
many
its
depressed level of cre-
section concludes with a discussion of the canonical set of policies that restore
macroeconomic
efficiency.
Section 3 turns to cyclical implications, and focuses more closely on the labor/capital
interpretation of the two factors
— where we take those
factors' distinguishing features to
be that the supply of uncommitted capital to form joint-production units to be more
elastic
^A number of recent contributions have examined various implications of appropriable quaisi-rents in
general equilibrium setting. Makowski and Ostroy (1995) highlight the key role that "appropriation" plays
in the eflBciency of markets. Ramey and Watson (1996) analyze the interactions of the holdup problem and
a matching model. More applied examples are MacLeod and Malcomson (1993), who
study the macroeconomic effects of employment contract forms that attempt to avert investment holdup;
Acemoglu (1996), who examines the effects of search-related incomplete contracting on human capital accumulation; and Robinson (1995), who looks at the economics and politics of labor-market institutions when
effort incentivization in
employment contracts are incomplete.
than that of labor. In
this context,
we show
that experiences market segmentation
at high levels of activity
shortages)
.
it is
(i.e.,
that, at low levels of activity, labor
there
is
the market for capital that
the capital market
is
when
the labor market
Put
segmented.
is
is
segmented
is
economy
will
(i.e.,
there are labor
excessively elastic (compared
segmented, and excessively rigid when
differently, recessions bring unnecessarily severe
unemployment, while expansions run into bottlenecks sooner than
particular, that the
efficient.
This implies, in
have an asymmetric response to a symmetric shock process
— with sharp recessionary dips and recoveries followed by shallow expansions.
this
asymmetry implies that an
We
Moreover,
macroeconomic shocks
increase in the volatility of
decrease average employment and output.
nature of the shock
the factor
involuntary labor unemployment), while
Moreover, the cyclical response of the economy
to an efficient economy)
is
conclude that while
will
— depending on the
— expansions may require stabilization or reinforcement,
recessions
should always be softened.
Section 4 touches on issues relating to the longer-term response of institutions and
technology to the presence of unprotected
factor will seek, as
specificity.
Prom a
political point of view,
an ex ante united group, institutional developments that increase the
other factors' specificity. But this pohtical incentive for rent appropriation has
because
it
each
its limits,
inherently results in ex post internal segmentation of the appropriating factor
between employed winners and unemployed
macroeconomic
inefficiency of
losers.
It
is
through that channel that the
opportunism enters into the
factor's political calculation,
and, beyond a point, starts dominating any additional distributional gain.
Over the long run, the economy
will also
respond along
attempt to circumvent the appropriability problem.
adaptation
ogy choice
is
is
in the relative factor proportions used.
essentially determined
its
technological dimension in an
A principal dimension of technological
We show how, in equilibrium, technol-
by the appropriated
factor.
That
factor,
we
argue, has
an incentive to reduce appropriation by selecting a technology that partly "excludes" the
other factor from joint production.
The
under-employment of the appropriating
result
is
factor.
a distorted capital-labor ratio and further
This exclusion phenomenon
with the role that capital-labor substitution seems to have played
is
in the rise of
consistent
European
unemployment.
Section 5 concludes with a series of macroeconomic questions that can be illuminated
by drawing on the ideas developed
in this paper.
An
appendix
follows.
Appropriable Rents
2
General Equilibrium
in
Factor Specificity in Joint Production
2.1
In this section
we
lay out the
model that we use to analyze the general-equilibrium implica-
tions of specific quasi-rents in the joint use of factors of production.
as given the institutional
framework and available technology.
It is
Our
basic
model takes
therefore appropriate
study of short to medium term equilibrium, but must be used more selectively in
for the
the study of long-term issues. Section 4 discusses the implications of endogenizing long-run
institutional
and technological
evolution.
Productive structure
Our model economy has one consumption good and two
and
factor 1
utility
2.
The two
factors of production, denoted as
factors are identified with optimizing agents,
from the consumption good, which we use
who
derive linear
as the numeraire.
Production takes place in two modes, identified with separate sectors of the economy.
Factors 1 and 2 can either produce separately in their respective Autarky sectors, or combine
in the Joint Production sector.
Autarky and by Ei
Each
factor's
For each factor
employment
total
Autarky sector
gate production function Fi{Ui).
is
i,
we denote by
Ui total
perfectly competitive
and characterized by an aggre-
In Joint Production, factors 1 and 2 combine in fixed
A
production unit combines xi units of factor
with X2 units of factor 2 to produce y units of the consumption good.
the total number of production units. Parameters a:i,X2
and
for
The
in
in Joint Production.
proportions to form "production units."
technologies.
employment
>
We
denote by
1
E
and y are given by available
implications of allowing for short-run substitutability between factors,
even greater substitutability in the long run through technological development will
be discussed in section
4.
Creation and destruction
We
study a one-period economy. There
were formed before the
factors of type 1
we
and
fix total factor
is
start of the period.
2,
a mass
There
E°
is
of pre-existing production units that
also
a mass U° and U2 of uncommitted
that are not part of a pre-existing unit. For each factor
z
=
1, 2,
supply to one:
XiE°
Production units that are newly created
+ f/° =
this period
1.
have
(1)
common
revenue y". Pre-existing
production units have heterogeneous revenues y°, whose distribution D{y°)
is
given by the
history of technology adoption and idiosyncratic shocks. Naturally,
minimum
revenue required for survival (see below)
of pre-existing units destroyed
The timing
of production
y°,
E°.
If
the
then the total number
D{y°).
is
is
denoted by
is
=
D{+oo)
as follows. In a first phase, pre-existing production units
decide whether to continue operation for this period, or to separate and release their factor
resources. In a second phase, factors that were released from pre-existing units
and uncom-
mitted factors can choose to form new production units, or remain in Autarky. In the
phase, factors in
A
new
number
sectors produce.
all
of identities will be useful in
units created,
final
and recalhng that D{y°)
what
is
the
C
number
follows.
Denoting by
number
of pre-existing units destroyed,
the
of
we have
E = E" + C-D{f);
= XiE-
(3)
= U°-x,C + XiD{f),
(4)
Ei
Ui
where
z
=
1,2.
The
first
(2)
identity equates the
number
E of production units
of pre-existing units plus net creation; the second gives Joint Production
each factor as a function of E; the
as a function of the
Specificity
When
number
of
last identity gives
uncommitted
factors
number
employment
Autarky employment
and net
to the
for
for
each factor
creation.
and incomplete contracts
factors join to
form a new production
respect to each other, and a share
the production unit.
If
(pi
6
[0, 1]
unit, they develop a degree of specificity
of factors
the factors separate, only
(1
i
—
=
with
1,2 can no longer be used outside
(l)i)xi
units of factor
i
can be used
elsewhere. Specificity can be a pure aspect of technology, or, as discussed in the examples
of section 2.2, can be due to institutional factors.
Specificity creates quasi-rents
factors within the production unit
whose value
and
is
the difference between the value of the
their value in their best outside use.
To guarantee
that specific quasi-rents will be divided according to the factors' ex-ante terms of trade, the
factors
unit
must enter an ex-ante contract that governs
and the division of
its
their participation in the production
surplus. Unfortunately, such ideal contracts are quite difficult
to achieve in practice.
In general, the contract must take into account the
ation. Specific investments are typically
made
full
complexity of the concrete situ-
not once, but incrementally throughout the
life
of a production unit.
The
contingent plan for making such investments, the duration
mechanism must be
of the relationship, and the rent-division
and made
fully contingent
that determine
on the future
pre-specified
profitability of the production unit,
on factors
evolving prospects, and on the various events, both aggregate and id-
its
The
iosyncratic, that govern each factor's outside opportunity costs.
specify the
from the start
many dimensions
that characterize each factor's participation in production,
again possibly based on contingencies outside the factors' control.
observability, verifiability, enforceability,
A
variety of problems of
and sheer complexity, make such
rarely possible. In practice, agents enter into arrangements
"incomplete contracts"
contract must also
— that leave plenty of room
ideal contracts
— what one might loosely
for ex-post discretion.^
call
(For a clear
discussion of incomplete contracts in the presence of specificity, see chapter 4 of Hart 1995).
When
pre-contracting
termined ex post.
It is
is
well
not possible, the division of specific quasi-rents must be de-
known
that, in this case, the relation
between the two factors
undergoes, in Williamson's (1985) term, a "fundamental transformation" from an ex-ante
competitive setting to an ex-post bilateral monopoly. To analyze the
contracting,
we
effect of
incomplete
distinguish between two extreme cases: the "efficient" equilibrium, where
factors are able to engage in full contractual
tracts" equilibrium,
where no precommitment
precommitment, and the "incomplete conis
possible.
Free entry and exit
We
can now turn to the determination of factor rewards
entry and exit decision rules for production units.
in Autarky,
any equilibrium with
<
Fim
for the
we denote by
and the
free-
pi factor z's rental price
we have
P.
in
If
in diflFerent sectors,
<
Ui
1.
=
Fim
(5)
Assuming the functional form
= —^\l-{l-U.)'+'/^^],
1
-I-
l/lji
L
Autarky production function, we get a constant
r,i>0,
J
supply-elasticity
r/j
for factor
i
into
simple transaction that would overstep the need for contracting altogether is an exchange of factors
own both factors in a production unit. In the first two examples we develop
below,
solution
is made impossible by the fact that one side of the transaction involves
this
in section 2.2
"inaUenable" human capital. In the third example, it is limited by span-of-control and other Umits to the
^A
that allows a single agent to
extent of vertical integration.
Joint Production:
Ei=p1\
=
z
l,2,
taking (1) and (2)-(4) into account. Naturally, Fi{Ui)
Turning to Joint Production, we
newly created production
unit.
To
tions are different for the efficient
to denote the former.
let zi;"
is
(6)
increasing and concave in Ui.^
denote the unit-compensation of factor
differentiate
and incomplete-contracts equilibrium, we use an asterisk
their ex-ante opportunity cost p*,
wr=pl
^
=
new production
governed by their ex-post opportunity cost
opportunity costs of
is
(1
—
units are
i.e.
l,2.
(7)
In the incomplete-contracts equilibrium, factor compensation in
such a production unit
in a
between variables when equilibrium condi-
In the efficient equilibrium, factors in
compensated according to
i
(f)i)pi.
The
new production
units
specific quasi-rent s"
is
from
the difference between the unit's revenue y" and the ex-post
its factors:
s"
= y" -
(1
-
(^i)pixi
-
(1
-
(J>2)P2X2.
(8)
Following the Nash bargaining solution for sharing the unit's revenue, we assume that each
factor
i
gets
its
ex-post opportunity cost plus half of the unit's bargaining surplus s":^'
<Xi =
(1
-
^i)PtXi
+
^s".
In the efficient case, the entry condition for the creation of
y">K^i+P2^2.
^
(9)
new
units
is
(10)
""The strict concavity of the Autarky production function implies the presence of a third "quaisi" factor.
This becomes relevant in the distributional analysis of section 4.1, where it is briefly discussed (see footnote
20).
^We impUcitly eissume that each type of factor in the production unit forms a coalition that bargains as
a single agent.
®An alternative specification of the "disagreement point" in bargaining yields the Shaked and Sutton
(1984) sharing rule that allocates ^y" to each factor 2is long as neither factor i = 1,2 receives less than
(1 — 4>i)piXi. (See Binmore, Rubinstein, and Wolinsky 1986 for a discussion of the foundational differences
between the two approaches). The discrete change in the way the opportiinity cost (1 — (i>i)piXi enters the
Shaked-Sutton rule makes it less attractive for an "aggregate" model. Otherwise, our main conclusions do
not depend on the specific sharing rule.
In the incomplete-contracts case, the rule for factor
w^>Pi,
It is
easy to show from (8)-(9) that (11)
y"
where
(10)
-^i
and
> PiXi + p^^X^i +
is
1
{(piPiXi
The
i.
this condition for factor
the term
Aj
Considering that the expression
relationship,
=
(t)iPiXi
(j>jPjXj
Aj measures the net
1,2.
(11)
-
^^iP^iX^i)
between the
difference
—
=
z
,
two
by
A=
|Ai|.
1, 2,
efficient
positive net specificity that
It is
is
entry condition
(13)
measures the value of what factor j sinks into the
effective specificity of factor
Ai
i.
Condition (12) for
is
positive
A-,j
obvious that
it is
if i
sinks in
= — A^, we denote
requires that revenues y" cover the
i
factors' outside opportunity costs, plus the net effective specificity
sink into the relationship.
(12)
(j)^ip^iX^i.
a greater value than the other factor, and negative otherwise. Since
their absolute value
is
equivalent to
denotes the factor other than
i is
=
to participate in Joint Production
i
Aj factor
i
would
the entry condition of the factor with
binding, so that, taken together for
=
z
1,2, the
two entry
conditions (12) are equivalent to
y""
>
PiXi
+ P2X2 + A.
(14)
We now turn to the separation decision of factors in pre-existing units.
To avoid clouding
the analysis with side-effects, we do not assume that pre-existing units exhibit any factor
specificity.
Otherwise, because factors would lose a fraction
factor supply
would
effectively
if
(pi
the unit separates, total
depend endogenously on destruction, and would therefore
not be fixed. Measuring the probability that a unit of factor
will
i
be employed in Joint
Production by
^^^^
^\^ur+xMry
the opportunity cost of factors in a pre-existing unit
unit to survive,
its
is
revenues must at least cover the
Xiwf
sum
-I-
of
(1
— Xi)pi.
its
two
For a pre-existing
factors'
opportunity
costs/ In other words, the free-exit condition for a pre-existing unit
"destruction margin" y°
y°
is
>
y°,
where the
given by
is
f = XiW^Xi + (1 - Xl)piXi + X2W^X2 + (1 - X2)P2X2.
By
equation
(7), in
(16)
the efficient equilibrium, the revenue requirement for survival reduces
to
f*=plxi+p*^X2.
Efficient
We
are
case.
(17)
and incomplete-contracts equilibrium
now ready
We make
to define equiUbrium in both the efficient
parameter assumptions that guarantee an
and the incomplete-contracts
"interior" equilibrium in
cases, so that free-entry condition (14) holds with equality
and
all
both
sectors have positive
employment.
Assumption
where Zy
is
is
y"
<
y"
<
2^
and E° <
2£;(y"),
= min{x,(l+(|)'""'),x.(l + (|)'""")}
defined implicitly by
=
xi^^/"^ 4/"^
The upper-bound
to drive
that
given by
..
and Z£{y^)
Equilibrium) We assume
1 (Interior
Zy
+ x^+^/'^ zl/'^ + max {xi+^Z"^ z^/^S x^+^Z"^ 4/^^ }
.
on y" guarantees that Joint Production revenues are not high enough
Autarky employment to
zero.
The upper-bound ze on the number E°
of pre-
existing units guarantees a need for positive creation.^
An
(interior) incomplete- contracts equilibrium
lo", 102, y°)
is
a set of variables (C, E, Ei, E2, Pi,
P2-,
that satisfies free-entry condition (14) with equality, as well as equations (2)-
(3), (6), (8)-(9), (13),
and
(15)-(16).
An
(interior) efficient equilibrium
is
a set of variables
(C*, £", E{^ E2, Pi, P2, Wi*,W2*,y°*) that satisfies the efficient free-entry condition (10)
^This separation rule
is
privately efficient.
Specific quEisi-rents give rise to the possibility of privately-
whenever there is a "non-transferabiUty" problem, due, for example, to asymmetric
information. See Myerson and Satterthwaite (1983) for a general result, and Hall and Lazear (1984) for an
inefficient separations
application to the labor market.
*This condition
is
stronger than needed at this stage, but
paper.
10
it
will
turn out to be helpful in the rest of the
with equality, as well as equations
(2)-(3), (6)-(7),
The
replaced by (C*, E*, E^, E2, Pi, P2, y°*)-
and uniqueness
for
and
(17) with (C, E, Ei, E2, pi, P2, y°)
following proposition establishes existence
both types of equilibrium (proofs
for all propositions
can be found in
the appendix).
Proposition 1 (Existence and Uniqueness) An incomplete- contracts equilibrium
ists,
is
unique,
and
unique, and satisfies
Assumption
1
employment
in Joint
C,Ei,Ui
satisfies
C*,E*,U* >
0,
i
>
=
i
0,
=
1,2.
An
ex-
efficient equilibrium exists,
is
1,2.
guarantees that equilibrium
is
characterized by positive creation and positive
Production and Autarky.
Before we turn to the basic implications of our model,
it
is
some
useful to look at
examples.
Examples
2.2
Specificity
and appropriable quasi-rents characterize a variety of transactions that are preva-
throughout the economy. Our highly stylized model can be given a number of
lent
We
pretations.
discuss three
main examples that touch on the
labor, financial,
inter-
and goods
markets.
Example
1:
Labor and capital
The two factors can be interpreted
prime example
3 and
4.
firm.
Autarky
or
in this paper,
and
as labor
will
and
be used
Joint Production consists of worker
employment
for
capital
in sectors that are relatively
is
employment and
immune
investment abroad, or consumption.
is
human
capital
is
the
capital investment within the
— voluntary or involuntary —
to contracting problems (and
example
Autarky
for capital
corresponds either to
(low
77fc).
typically sink various forms of specific investments into their relation-
ship (see Becker 1964, for example).
or
This
We think of labor as the relatively inelastic factor
relatively elastic (high
Firm and worker
l,k).
the "informal" sector, where constant returns and low
capital requirements allow for self-employment).
while capital
=
specifically to develop the analysis in sections
workers corresponds to "unemployment"
typical of the developing world
77/),
(now denoted asi
embodied
(j)k
>
in the worker.
instead? Possibly because the investment
is
arises
Why
when
the firm finances organizational
does not the worker make the investment
firm-specific as well as worker-specific,
and pos-
sibly because the worker does not have sufficient wealth (and cannot obtain competitive
11
outside financing for the same incomplete-contracts reasons that render the firm's invest-
ment appropriable).
>
</>/
when the worker
arises
opportunities to firm-specific knowledge.
A
dedicates part of his lifetime learning
special case of firm-
and worker-specificity that
has been studied extensively in the labor-market literature are search costs expended by
and workers, which, by
firms
their very nature, cannot
be protected by ex-ante contracting.
Generally, one expects each side to make, over time and in various ways, investments that
are specific to the other, so that both 0/ and
Specificity can have
dimension.
With
legislation.^
The power
unions,
it is
Legislation on dismissals
of the union.
The
institutionally-driven specificity.
A
2:
it
takes,
would
The
origin, in addition to its technological
who
are able to form a union to
of the union
may
derive from firm investments
— again, ultimately a contracting problem — or
become
relationship-specific
full set
of
and enter the scope
and severance pay provides another example of
imposition of severance pay, for example, depending
effectively increase
(f)^
or reduce
(j)i.
External finance
second interpretation
firms.
positive.
not only worker-specific investments but the
firm- or industry-specific capital that can
Example
be
Consider, for example, the case of workers
that are embodied in workers as a group
on the form
will
an important institutional
negotiate with their employer.
from
(pk
first
entrepreneurial
factor
skills;
is
Moore
1994). If
serious
damage
it
above as modelling the external financing of
would then represent "managers," who possess management and
the second factor would represent the capital of outside financiers
(shareholders and lenders).
agement makes those
to think of the
The
delegation of control rights over the firm's assets to
assets partly
management- specific
(e.g.,
Williamson 1988; Hart and
withdraws from the relationship, management can,
to the firm's value
acts of omission or commission.
The
its assets,
different
ways
in
(see, e.g., Shleifer
cause
capital,
or undertaking highly disruptive
which financiers can protect the
value of their investment from management appropriation
governance" approach to finance
in various ways,
— by withdrawing their firm-specific human
withholding vital information on the firm and
man-
is
the subject of the "corporate
Although we do
and Vishny 1995).
not emphasize this interpretation, our results can help shed light on the macroeconomic
implications of financial constraints (see Caballero and
®See, e.g., Lindbeck
the
phenomenon
and Snower
of "strikes."
—
1996c)
(1986). In this context, appropriability finds its clearest expression in
The only reason
for technological or legal reaisons
Hammour
strikes
put any pressure on employers
to substitute outsiders for striking insiders,
of specificity with respect to labor. That
is
precisely the leverage used
12
i.e.
is
that
it is
capital has
costly
—
some degree
by insiders to improve their
deal.
Example
A
3:
Vertical relationships
third example draws on the role of specificity in the hterature on vertical integration
Klein, Crawford,
(e.g.,
and Alchian 1978). Our two
factors
would then represent the capital
of upstream suppliers and of downstream customers, respectively.
make mutually
that
is
specific investments
specific to
>
((^j
a suppher (by locating
An
0).
Buyer and
may
electric utility
seller
may
invest in a plant
near a coal mine, for example) or specific
it
to a customer (by locating near an industrial complex).
A
are "customer markets," where the upstream supplier
a final-goods producer and the
downstream customer
(e.g.,
Phelps and Winter 1970).
Under-employment and Rationing
2.3
A
a consumer
is
is
example
special case of this
microeconomic situation where one factor
is
open to appropriability by another,
if
widespread throughout the economy, results in offsetting macroeconomic adjustments to
guarantee that appropriated factors obtain adequate returns in general equilibrium and
satisfy their free-entry condition. This general-equilibrium response affects
of the macroeconomy, which appear as
symptoms
of an inefficient
major aspects
macroeconomic
"solu-
tion" to the unresolved appropriability problems. This section describes general-equilibrium
implications for factor employment.
The main benchmark
We
start
for
an incomplete-contracts equilibrium
by giving parameter conditions
is
an
efficient
economy.
for the incomplete-contract equilibrium to
be
efficient.
Proposition 2 (Balanced Specificity) The incomplete- contracts equilibrium
iff,
is
efficient
in equilibrium,
(plPi^i
which
will
happen
iff
the
\(f)i
Condition (18) for efficiency
it
is
+
(j)2
(18)
(t>2P2X2,
economy 's parameters
Xi
other words,
=
satisfy
X2\(pl
Xi J
+ (f>2X2j
equivalent to requiring zero net effective specificity A.^° In
requires that, even though factors
may
sink
some degree of
specificity
with
^"Throughout we eissume the two factors' bargaining share parameter to be equal. If not, the efficiency
me modified by dividing each side of (18) by the bargaining share of the corresponding
condition must
factor.
13
respect to each other, their interdependence be "balanced."
To
interpret this balanced-specificity condition, note that effective specificity (piPiXi
determined not only by the
E^^. A
low
is
X2
factor with unattractive outside opportunities in
When
the factors are completely symmetric
— condition
—
(19) for balanced appropriation holds.
i.e.
be
(i)
the factor with the lower elasticity
rji.
symmetric, the appropriating factor
(ii)
What
The
is
will
the effect of appropriability
first effect
of appropriability
if
=
has relatively
sinks into the relationship
(f)i
=
(f>2,
iji
=
772
and xi
specificity. If
=
comes
everything else
the factor with the lower specific share
is
(piXf,
the efficient parameter condition does not hold?
to reduce the
is
it
pi)
Positive net appropriation
from asymmetries in the parameters that determine factor
and
Autarky (low
because the relative value of what
effective specificity,
low.
but also by the factor's Autarky reward p,
specific share (piXi,
is
Proposition 3 (Under-employment) In an
employment
level in Joint
Production:
inefficient incomplete-contracts equilibrium
both factors are under-employed:
Ei<E*,
Underemployment
results
Joint Production, since
Pi
= w^
its
=
1,2.
from the decreased incentives of the appropriated factor to enter
it is
that factor's entry rule that holds with equality. Equalization
Autarky and Joint-Production returns
of the appropriated factor's
partly by depressing
2
own opportunity
cost pi
is
achieved
and partly by reducing the appropriating
both of which involve a reduction in Joint-
factor's opportunity cost p-,i (to support lo"),
Production employment.
The second
implication of appropriability
is
market segmentation of the appropriating
factor:
Proposition 4 (Market Segmentation) In an
rium,
let
i
be the
"appropriated" factor
while the market for the other factor
Net appropriation involves one of the
is"
=
for that factor.
(pjPjXj (see equation 9),
i.e.
A^
>
0.
The market for factor
and
w^i>p-,i.
factors capturing rents,
To
its
i.e.
i
clears,
segmented:
is
wf=pi
market segmentation
—
inefficient incomplete- contracts equilib-
(20)
which inherently induces
see this, note that the market for factor j clears
iff
share of specific quasi-rents exactly compensates
it
14
what
for
it
sinks into the relationship. Since ^s" goes to each of the factors, both markets
clear simultaneously only under balanced specificity,
Otherwise,
equilibrium,
equality.
let i
it is
The
replacing |s"
be the appropriated factor (Ai
obvious from (12) that
other factor market
=
it is
>
factor
when equilibrium
is
efficient.
Given that we have an interior
0).
free-entry condition that holds with
z's
segmented, and
is
i.e.
its
return differential
is
obtained by
4>iPiXi in (9) for factor -li:
«,-p.i)x^i =
Thus, taking A/x-,j per unit, net
Ai.
(21)
measures the extent of the appropri-
effective specificity
ating factor's market segmentation.
Net appropriation gives
rise to
the "involuntary" unemployment of the appropriating
factor in Joint Production, which persists because that factor cannot
pensation lower than equilibrium
determined by the appropriated
w'^^.
The number
precommit to a com-
of "slots" open in Joint Production
factor's free-entry condition,
is
and are rationed among units
of the appropriating factor.
Productive Sclerosis and Unbalanced Gross Flows
2.4
Besides the level and structure of factor employment, appropriability affects the manner in
which production units restructure
The
in response to evolving profitability.
following proposition states that the inefficient
rosis," in the sense that pre-existing units are
itability
than
in
an
efficient
economy
exhibits "productive scle-
kept in operation with lower levels of prof-
economy.
Proposition 5 (Sclerosis) An
inefficient incomplete- contracts equilibrium exhibits "pro-
ductive sclerosis":
The scrapping margin
To
in
an
inefficient equilibrium
is
lower than in an efficient equilibrium.
see why, rearrange expression (16) for y° taking the accounting identity y"
W2X2
=
w^xi
+
into account:
y°
=
y"
-
(1
-
Ai) (u;^
Since in an efficient equilibrium there
the efficient scrapping margin
is
y°*
=
- pi) xi -
is
(1
-
A2) {w^
- P2) X2.
no market segmentation
y". This
15
is
(lu"*
(22)
=
p^, j
=
intuitive, since pre-existing units
1,2),
can be
costlessly replaced
On the other hand,
by new units that produce y".
factor in an inefficient equihbrium, the market for factor
and
> p-,i) and expression (22)
(ii;"i — p-,i) x-,i < y" (since A-,j <
A-,i)
in
1
an
be segmented
=
(u;"
=
pi
—
(1
—
y"
interior equihbrium). In this case, the outside
opportunity cost of the factors in a pre-existing unit
of factor
will
scrapping margin becomes y°
for the
it;"j
->z
the appropriated
if i is
than y" because released units
is less
are not guaranteed a slot in Joint Production and, with probability 1
-iz
may end up
in
Autarky earning
Sclerosis
less.
A-,i,
thus tightly related to factor-market
is
segmentation. Coupled with under-employment,
—
it is
likely to constitute
a powerful drag
on economic growth.
The next
We
proposition characterizes the efficiency of the gross flows of production units.
define aggregate income as
W(C,y°)
=y"C+
/
where the argument
^
rdDir)+
'r
in function Fi{Ui)
is
- x,C + XiD{y")).
obtained by replacing
states that, in an inefficient economy, creation
is
(23)
(see Caballero
and
The
(4) for Ui.
proposition
generally insufficient and destruction
excessive. This captures an important dimension of
nomic adjustment episodes
Fi{Uf
i=l,2
"employment
Hammour
Proposition 6 (Creation and Destruction) An
crises"
is
during macroeco-
1996a and 1996b).
inefficient incomplete-contracts equi-
librium exhibits insufficient creation:
dW
dC
and
^
>0;
excessive destruction:
dWInsufficient creation
is
<
due to the
when
D'{f) >
0.
fact that the appropriated factor
centives to enter Joint Production because of positive net appropriation.
positive density D'{y°)
struction
is
>
it is
has reduced
When
there
inis
a
of pre-existing units at the destruction margin, excessive de-
due to the excessively high compensation of the appropriating
Production, given that
i
involuntarily unemployed.
side opportunity cost of a unit of factor
from a private point of view,
it is
-'i
From a
16
+
-iz
in Joint
social point of view, the out-
in a pre-existing unit
higher and equal to p^i
factor
is its
X^i {w-,i
Autarky reward
— P-^i), which
p-.^;
values
the possibility of capturing specific rents in a
what causes destruction
to unproductive labor
that case
It
is
zero,
to
unemployment
and any
may appear
be excessive.
positive
0).
case arises
The
when Autarky corresponds
social opportunity cost of labor in
too high and results in excessive destruction.
is
a comparison with the efficient equilibrium; and the latter
a comparison between the social and private values of a pre-existing unit in the
equilibrium.
The
is
paradoxical that the economy exhibits both sclerosis and excessive de-
struction. In fact, the former
is
is
=
This high private compensation
unit.
An extreme
{p^i
wage
new
inefficient
coexistence of "sclerosis" and "excessive destruction" uncovers the fallacy
way
of a "liquidationist" approach in our context, that would see in a recession a healthy
of cleansing the productive structure from sclerosis (see,
sense in liquidating sclerotic production units
if
e.g.,
De Long
There
1990).
is
no
the released factors will not be reabsorbed
in Joint Production through an adequate creation rate.
Dual Optimal Policy Design
2.5
We now
turn to the problem of designing a canonical set of optimal macroeconomic policies
to address the macroeconomic
ills
of appropriability.
Those
policies are not designed to
address other inefficiencies due to appropriability that arise at the microeconomic
We
define two types of canonical policies: creation incentives
added to the revenue
new production
of each
unit;
replacing y" in entry condition (14) by y"
-|-
which are subsidies
cr",
and protection subsidies
the revenues of each pre-existing unit. Equilibrium in this case
is
level.
a°,
added to
determined as before, by
a", and y° in exit condition (16) by y°
Proposition 7 (Dual Optimal Policy) Efficiency can
be restored in
+ a°
an incomplete-contracts
equilibrium with the following combination of a creation incentive and a protection subsidy:
cr"*
where
-iz
= A*
and
denotes the appropriating factor
The reason we need a dual
quasi-rent appropriation
—
is
(i.e.
a"*
^
A-,i
<
\*_,iA*,
0).
policy approach even though there
that this
ill
only one
ill
— namely
affects different types of agents differently.
are two types of marginal decisions in this economy: creation
tives for creation are depressed
is
There
and destruction. The incen-
by A, which must therefore be compensated
for.
At the
destruction margin for pre-existing units, the prospect of rent appropriation also distorts
the opportunity cost of the appropriating factor. But this distortion
17
is
only equal to the
rents
A times the probability A*
lower
if
that they will be captured. That distortion would be even
the factor had to scrap some specific component upon separation. In any case, the
protection subsidy a°* must therefore be lower than ct"*.
What
to
mend
the need for two policy tools implies in practice
is
that, alone, a policy designed
would exacerbate excessive destruction by increasing rents
itself,
A
things on one margin will exacerbate things on the other.
of capturing those rents.
A
protection subsidy, by
itself,
creation incentive, by
as well as the probability
would reduce destruction but make
the private factor costs of creation even higher. Only a combination of the two can restore
efficiency.
An
^^
application of this approach to the problem of managing macroeconomic adjustment
can be found in Caballero and
Hammour
(1996b). In that paper,
must be managed through a combination of creation
for the existing structure.
A
that adjustment
and protection measures
incentives
purely gradualist approach, which can be thought of as a
single policy-instrument approach to slowing
address
we argue
down
creation,
is
deficient in that
it
does not
— and actually exacerbates — the need to accelerate creation.
Business Cycles: Slack and Bottlenecks
3
In this section
we analyze the
effect of
unprotected specificity on the economy's response
to aggregate shocks. Although our simple setup does not allow a
yields important insights into the economy's cyclical features. ^•^
exogenous shock to gross revenues y", which
tals" or
(e.g.,
may be due
a tax on gross output). ^^
We
focus
is
more
closely
is
analysis,
it
economy's "fundamen-
or "aggregate supply" type
on the capital/labor interpretation
main distinguishing feature between
that the supply of (uncommitted) capital
Assumption 2 (Capital/Labor) The
demand"
dynamic
We consider the effect of an
either affect the
to a distortion of the "aggregate
of our two factors. For our purposes, the
labor
may
full
relatively
more
elastic
capital
and
than labor.
two factors are capital (k) and labor
(I).
We
^'^There are many ways to implement the above "canonicEil" policies, taking into consideration the economy's regulatory and institutional context in which they operate. For example, if new and pre-existing
units cannot be segregated by policy, the above can be replaced by a production subsidy a^ and a creation
subsidy 0-'=: a^' =a°' and cr"' =a"' -a^'.
^^A dimension that our setup is ill designed for is the analysis of gross employment flows over the cycle,
which requires a full inter-temporal analysis. We examine this question in Caballero and Hammour (1994,
1996a).
^^The shock may or may not
affect the revenues y° of pre-existing units.
analysis of gross flows over the cycle, which our setup
is
18
This would be relevant for an
not designed to address.
assume
that
exhibit
some
uncommitted
capital
is
m.ore elastic than labor,
and that both
capital
and labor
specificity:
Vk>m\
and
(f)k>0
(24)
(pi
>
0.
(25)
Unemployment and shortages
How do
factor
employment patterns evolve over the
cycle? First,
it is
easy to show that,
as expected, higher levels of revenue are associated with higher levels of Joint-Production
employment:
dE
^
3—
More
>0.
interestingly, the following proposition states that, as revenue
the economy turns from a situation where the labor market
Production investment
is
is
<
satisfies balanced-specificity condition (19).
y"'' the labor
market
y"^ corresponds to the
is
is
segmented;
if y'^
below
y^^ the capital market
>
y"** capital is
of labor-market shortages
economy
is efficient.
crosses the level of activity y"**,
unemployment and
and segmentation
where capital could obtain a higher return
to find the requisite labor. -^^
is 1
which there
At
it
levels of
appro-
is
turns from a
capital shortages for job-creation, to one
in capital markets.
should one interpret the possibility of segmented capital markets?
units, Tobin's g
segmented.
appropriated, while at levels higher than y"*" labor
situation of involuntary labor
How
is
level of revenues implicitly defined in proposition 2, at
As the economy expands and
priated.
exists a level y"'' of revenues
In an incomplete- contracts equilibrium,
zero net appropriation and the incomplete-contracts
activity
segmented and Joint-
factor.
Proposition 8 (Unemployment and Shortages) There
ify^
rise,
the limiting factor for expansion to a situation where capital
segmented and labor shortages are the limiting
y" that
is
and employment
It is
a situation
invested in Joint Production but
if
is
unable
In terms of the stock-market valuation of Joint-Production
when y" <
y"*"
and greater than
''*One expects contracting problems to be less severe
when
1
labor
when y^ > y^^
is
(even though there
appropriated than when capital
is.
The
appropriated, some capital may
be transferred to the worker to convince him to commit to a production unit; when capital is appropriated,
the reverse transfer of labor to capital is infeasible. Although, in practice, this may not constitute a perfect
solution because of asymmetric information and other re£isons, it gives reason to believe that capital-market
reason
is
that labor
segmentation
is
is
more
"inalienable," while capital
likely to
is
not. Thus,
when labor
be alleviated at the microeconomic
19
level
is
than labor-market segmentation.
are no explicit adjustment costs). Periods of labor-market shortages are times of expensive
stock-market valuations.
Although the
level of revenues y"*"
seems arbitrary, we argue
in section 4 that, in the
long run, institutional and technological evolution are likely to result in a situation where
y"'' is
within the range of revenues in which the economy fluctuates. Institutions are likely
to respond to correct any imbalance in appropriation that cause macroeconomic inefficiency
beyond a certain
to rise
point;
and technologies
will also
be developed that allow
On
production with new factor proportions that reduce this imbalance.
does not expect
y"** to
be far removed
both counts, one
run from the economy's average
in the long
efficient
level of
output.
The next
proposition characterizes the economy's cyclical responsiveness at different
levels of activity.
Proposition 9 (Elastification/Rigidification) The economy's
tified"
when
the labor
market
is
cyclical response is "elas-
segmented, and "rigidified" when the capital market
is
segmented:
^^
PW'
I
When
dE*/E*
(
^
dy^/y-
„.
„
,
'^'"
'^
(26)
>y
y
'}
'
economy
labor suffers from involuntary unemployment, the incomplete-contracts
more responsive
to shocks than an efficient economy;
economy's cyclical response
is
more
rigid
than in the
when
labor
the short factor, the
is
efficient case.
is
Thus, appropriability
exacerbates recessions and brings about unnecessarily severe and involuntary unemploy-
ment, while
it
constrains expansions by creating labor shortages that prevent sufficient
investment in new jobs. The balanced-specificity level of employment E^ associated with
y"*" is
analogous to the concept of a "natural rate."
It is
the level of employment at which
the labor market functions effectively within the economy
cessive slack of involuntary
—
it
neither builds
unemployment nor constitutes a bottleneck
up the
ex-
for the rest of the
economy.
An intuition for why proposition 9 holds can be drawn from the under-employment result
(proposition 3).
As
illustrated in figure
incomplete-contracts economy
employment
^Figure
1
is
is
1,
we know
that
when
y"'
= y"'''
employment
equal to that in the efficient economy, while for y"
lower than efficient on both sides of
was generated with the following parameter
20
y"*".^^
values:
Xk
Thus
=
as revenues
0.7, x;
=
1.4; T]k
=
in the
7^
y"
expand and
8.0,
r]i
=
0.3;
0.0
0.1
0.2
0.3
0.4
0.5
0.9
C
m
<
D
o
o
0)
(-1-
fD
I
n
o
r-^
-i
D3
O
r^
W
n
£)
-J
3
employment
cross y"'',
it)
to the
sides
left
expands
first
faster
than in the
of y"**, then expands slower (to
under-employment
At low revenue
levels
is
it is
economy
up with
(to catch
short again) to the right of
fall
y"''.
On
both
due to one of the factors constraining employment of the other.
capital
— the more
elastic of the
free-entry condition constrains labor employment,
economy's response; while
efficient
at high revenue levels,
two factors
— whose binding
and induces excessive
it is
labor
— the
elasticity in the
less elastic factor
— that
constrains growth and induces a rigid response.
Two
interesting implications follow from proposition 9.
of Jensen's inequality. Because of the
at low
and high
levels of activity,
asymmetry
an increase
a simple application
first is
economy's cyclical responsiveness
in the volatility of aggregate shocks
inefficiently lowers average Joint-Production
can lead to high costs of macroeconomic
in the
The
employment and output. This
around y" ^
"level" effect
instability.
Second, the economy will exhibit an asymmetric cyclical response to a symmetric shock
process. Figure 2 gives a stylized representation of the model's implications for symmetric
cycle in revenues around y"*".^^
The two
curves represent the sequence of (static) equi-
librium employment levels that correspond to each revenue level over the cycle, with the
curves' averages
efficient
shown
as a straight line.
economy, which
is
The dashed curve
represents the response of an
symmetric around the average employment
curve represents the response of the incomplete-contracts economy.
level E''.
It is
The
solid
asymmetric, with
excessive elasticity at low activity levels and excessive rigidity at high activity levels, and
exhibits lower average log-employment than the efficient economy.
pattern
is
reminiscent of asymmetries documented for the
apparent asymmetry
in the
US
The
resulting cyclical
business cycle, such as the
economy's response to negative and positive
Sichel (1992), for example, characterizes post-war fluctuations in
US
oil-price shocks.
output as consisting
of three phases: contractions, high-growth recoveries to pre-recession levels, and moderate-
growth periods. The corresponding pattern
in figure 2 are the relatively
recession-recovery phases below average E, and the shallow and
moderate expansion above
sharp and short
more prolonged phase of
it.
Stabilization policy
There
is
a strong case for trimming recessions in the presence of appropriability, irrespective
of whether the adverse shock affects fundamentals or
4>k
=
^®
0.4,
4>i
=
is
due to an aggregate distortion
0.2.
Figure 2 was generated with the same parameter values as figure
21
1.
—
0.58
0.54
o
b
1
1
1
^>^
0.74
^^'
1
'
0.7
'
^
^^y
o
^^/
^
/ /
*^
y
o
CO
f
{
/
C
\\^^\
bo
-i
\
O
fV)
^\\
^"^«<\
1-
b
TO
1
\
\
1—
1
c
^^^<:nj^
o
1
7'
Vj^
%.
fO
o
0.70
0.66
0.62
1
1
b
o
o
1
ro
o
\:
"
*-
P)
V
1
?d
fD
fO
\
'co
CO
5"
2
g
3
2:
T3
3
"
T3
O
M
fD
/
/
n
~
\
1
(t
CO
b
M
\
1
/^
'
1
CO
n-
1
m
*.
1
1
,
1
yy
^
"
i.e.,
whether
affects the "central planner"
it
brings employment below
unemployment and
E'',
sclerosis
is
problem or not.
When
proposition 7 indicates that the optimal response to labor
to apply creation
and employment
more necessary
in the presence of a distortionary shock, since
not contract at
all in
The appropriate
distortionary,
it
a shock to fundamentals
an
incentives. This
efficient
policy response during expansions
should be stabilized. However,
£J"'',
if
is
economy should
more ambiguous.
the favorable shock
is
If
the shock
Thus, while recessions are always
to fundamentals
it
to
inefficiently severe,
expand beyond
expansions
may
well be "golden opportunities" that call for reinforcement rather than stabilization.
this sense, recessions should
Institutional
In
be systematically trimmed, while much greater care should be
taken not to curtail real opportunities
4
is
proposition 7 again prescribes a combination of ex-
pansionary incentives that reduce the economy's bottlenecks and allow
"natural" rate.
the
that case.
and takes the economy beyond
its
is all
for expansion.
^^
and Technological Evolution
In the short term, factors' net specificity Aj varies mostly as a result of the general-
equilibrium response of Autarky prices to changes in macroeconomic conditions. Over the
medium and
long term, however, institutional and technological forces are likely to directly
affect net specificity
substitution {xk/xi).
through changes
in unitary specificity (the
4>i^s)
and through factor
This section explores the long-run institutional and technological
responses to the problem of appropriabihty.
4.1
An
Institutional Balancing
Act
Institutions arise as the rules that govern the transactions between agents or groups of
agents.
At the
level of individual transactions
between workers and
firms, institutional
arrangements often arise as ways to improve efficiency by alleviating appropriabihty problems and "minimizing transactions costs." Institutions also develop to regulate interactions
between "coalitions" of labor and capital owners, be
(e.g., firm- union
it
at the level of corporate
governance
bargaining or corporatist representation) or at the political level through
the legal and regulatory environment
(e.g., right-to-strike
or severance-pay legislation). In
^^See De Long and Summers (1988), e.g., for a related view of business cycles as "repeated transient
and potentially avoidable lapses from sustainable levels of output" and of good policy as aiming to "filling
troughs without shaving peaks"
(p. 438).
22
this function, institutions
can play a distributional as well as an efficiency
role,
and embody
the entrenched interests of different groups. ^^
This section
tries to
account for the labor and capital interest-group incentives to develop
institutions that affect their
mutual
driven by distributional concerns,
very fax from balanced
The
politics of capital
"specificity."
Although
interest
groups
we argue that the institutional outcome
is
may be
strongly
unlikely to drift
specificity.
and labor
Institutional arrangements can reinforce the effective specificity of one factor with respect
to another by allocating rights
by making otherwise
the right not to lose one's job "without cause") or
feasible contracts unenforceable (e.g., the unenforceability of
commitment
to long-term
dimension of
specificity,
is,
(e.g.,
employment
we think
(pi^s
as having an institutional
to a large extent, a political choice variable.
changing the
In order to capture this institutional
contracts).
of the
We
(pi^s.
We view
period in our model as representing the long run.
that pulls evolutionary forces.
From
this perspective, initial conditions
3 (Long
Run)
There are no pre-existing units:
gregate income of each of the factors. Under assumption
Wi
term
second term
of the single
this "long run" as
E°
In order to get to the incentives of different interest-groups,
first
we think
matter
an attractor
less
and we
that there axe no pre-existing units:^^
Assumption
The
component which
analyze different groups' interest in
Since institutions typically take time to evolve, at this stage
may assume
worker
is
is
= wfEi+piil-Ei),
the income of units of factor
the income
of units in Autarky. ^^
i
3, it is
0.
we denote by Wi the
ag-
easy to see that
i^l,k.
engaged
The
=
in Joint
(27)
Production, and the
interest of factor
i
as a whole
is
to
'^Recent analyses of the politics of institutional development include Robinson (1995, 1996), who analyzes
Roe (1994), who gives a political interpretation to the origins
the politics of labor-market institutions; eind
of US corporate governance arrangements.
^^Thus, we view pre-existing units as powerful enough to aflFect the time and speed at which institutions
evolve and, perhaps, the precise limit to which institutions converge, but not powerful enough to change
the baisic course of long-run institutional developments.
W
as defined in (23). The difference corresponds to the
^°Wi + Wk do not add up to aggregate income
income X^ _, t ^t(f^i) —pdJi that accrues the "shadow" factor implicit in our decreasing-returns assvunption
on the Autarky production functions Fi{Ui). We do not consider the political incentives of this third
"factor."
23
maximize Wi, but there are distributional
The argument
segmentation.
for
issues within each
maximizing Wi
factor's unconditional expected income.'^^
We
group in the presence of market
in the "long run"
is
that
represents the
it
also analyze the ex post incentives of factor
owners in Joint Production and Autarky.
Proposition 10 (Interest Groups) For each factor
finding the pairs
{(f)i,(j)k)
G
[0,1]'^
i
=
I,
k,
consider the problem of
maximize the ex ante aggregate factor income Wi
that
arising in the corresponding incomplete- contracts equilibrium.
There
(i)
is
a line segment that crosses the parameter space
which any point maximizes Wi. To
measure
A=
A'''
>
A -unit
for any pair
of factor
{(f)i,(t>k)
S
i
E=
i,
and a unique
pi,
which
first
part of this proposition states that each factor
z,
as a whole,
institutional arrangement that creates in equiUbrium net specificity
factor has
an incentive to capture rents
conomic outcome. There
is,
in fact, a
level of net specificity (recall that
along this fine
may
ment.
It is
not
Aj
whole
=
i
and falls
(f)-,i
would choose an
A^ >
in its favor.
at the cost of a socially less efficient
line in
(piPiXi
accommodate
difficult to
in the short
—
(<?!);,
macroe-
<^fc)-space
that yields any desired
The
different configurations
(p-^ip-^iX-^i).
—
i.e.,
run changes in the macroeconomic environ-
conceive of situations where the historical evolution process does
not lead to the most "flexible" configuration
—
i.e.,
the configuration with the lowest
</>/
(pk-
The
this
maximized
correspond to widely different degrees of institutional "rigidity"
different abilities to
and
is
(pi.
The
The
level of
that yields an efficient equilibrium; while a unit of factor
employed ex post in Joint Production receives wf, which always increases with
with
and along
[0, l]'^
£jW.
employed ex post in Autarky receives
[0,1]'^
6
points on that segment there corresponds a unique
all
of net effective specificity in favor of factor
Joint-Production employment
(a)
{(pi, (pk)
is
political incentive for each factor to appropriate rents has its limits.
The reason
for
stated in the second part of the proposition. Inherently, a factor's attempt to capture
rents results in own-market segmentation, and creates winners and losers within the interest
group.
The winners
are "insiders" employed in Joint Production,
whose ex post incentive
'"^We assume that interest groups recognize the general-equilibrium impact (on pi's and A^'s) of their
Although "partial-equilibrium myopia" can undoubtedly play an important role in the
political choices.
political process,
our assumption captures the idea that interest groups
adjust to the general-equiUbrium consequences of their choices.
24
will partly anticipate
and partly
who remain
from rent appropriation
is
unlimited; the losers are "outsiders"
whose ex post incentive
is
to minimize macroeconomic inefficiency. It
in
Autarky, and
therefore through
is
the internal segmentation of the appropriating factor that macroeconomic efficiency enters
its
ex ante objective function and limits
The
incentive for rent appropriation.
degree to which institutions can deviate from balanced specificity
bounded.
At*^l
its
If in
the long run political power
lies
with ex ante interest groups,
represent upper bounds on capital's and labor's long-run net specificity.
limits,
both factors would attempt to reduce the degree of appropriation
It is in this
sense that
we expect
is
institutional forces to
A'''
and
Beyond those
in the
perform a "balancing
therefore
economy. ^^
act,"
and keep
the economy from deviating too far away from balanced specificity.
Institutional rigidity
Institutions are slow to evolve
ipate them.
Even though
would eventually lead
large
and adapt, and they often react to
and persistent changes
in the
to institutional adjustment, in the
crises rather
than antic-
macroeconomic environment
meantime
it
is
proposition 8
(unemployment/shortages) that determines the fortunes of different factors of production.
Suppose, for example, that the political outcome leads to a situation of balanced specificity
for
will
a certain expected
level of y".
be segmented; and
if
If realized
realized y"
is
y"
is
less
than expected, the labor market
more than expected, the
capital
market
will
be
segmented.
This mismatch between the frequency at which institutions react and that at which
shocks occur, together with our analysis of the incomplete-contracts economy's response
to shocks, naturally
fits
with accounts of European macroeconomic performance in the
postwar period. The European experience
in the fifties
and
growth (high y") allowed the development of welfare-state
in its relationship with capital (high
resistance
on the part of
without
(pk)
capital. In fact
much
sixties
was one where vigorous
institutions that benefited labor
cost in terms of
Europe exhibited
signs of labor shortages during
that period, which necessitated a substantial flow of immigrant labor.
eighties
tivity
(volatile
and low
y").
The
a burden on the labor market and gave
The
seventies
and
policy,
and produc-
institutions that evolved after the
war became
were a period of negative aggregate shocks, often contractionary
slowdown
unemployment or
rise to
a serious unemployment problem (proposi-
argument why a highly inefficient political outcome is unlikely to persist,
an analysis that attempts to unify the view that government favors interest groups with the view that
government corrects market failures. Taking an economic approach to political behavior, he argues that
pressure groups benefitting from activities that raise efficiency have an intrinsic advantage in the competition
for influence over groups harmed by those activities, and therefore will lobby more efiFectively for efficiency.
^•^Becker (1983) provides another
in
25
tion 8).
The
institutional
framework has responded, but quite slowly as
"insiders." Unions, for
from secure
example, are today
it
faced resistance
much weaker than they used
to be.
Technology also seems to have adjusted with substantial capital-labor substitution, a point
we come
to in the next section. In the meantime, proposition 7
recommends introducing
large job-creation incentives, while the requisite "protection subsidies" are probably
than provided
for
by existing job-protection
legislation (which, unlike
the unfortunate effect of effectively increasing capital specificity)
more
pure subsidies, have
.^^
Technological Development: Factor Exclusion and Withdrawal
4.2
Although
fixed in the short run, technology
is
a major dimension along which production
units can adapt to the appropriability problem. In this respect, a central aspect of tech-
nology
is
relative factor intensity.
factor substitution in the short run,
menu
Even though
new
long run. This section asks the question,
Our
we consider an extreme form
fixed proportions in the short run
priability problem,
and how
will that
may
allow limited
technologies can be developed that allow a broader
of factor intensities. In this paper,
and assume
available technologies
how
and
will
of this dichotomy,
infinite elasticity of substitution in
the
technology choice respond to the appro-
response in turn affect macroeconomic equilibrium?
analysis can also be used to shed light on the consequences of allowing
some
factor
substitution in the short run.
Technological possibilities
From a
we assume a
long-run perspective,
technological
menu
characterized by a constant-
returns function y"(xfc,x/) that essentially relates productivity to relative factor intensity;
and a function
(pi{xk,xi),
i
=
k,l, that is
homogeneous of degree zero and
specificity to relative factor intensity (see below).
so y" and
(j)i
development.
relates unitary
In the short run, Xk and xi are fixed,
are fixed; in the long run, those variables result from technology choice
We
and
assume the following functional forms.
Assumption 4 (Technological Menu) The
long-run technological
menu
is
characterized
by
y'^ixk.xi)
=
\a{xk+xi),
a>0;
^^Some countries have opted for increeised unemployment benefits, which amounts to subsidizing the segmented factor's Autarky sector and exacerbates the appropriability problem. This mechanism, it is argued,
may have played an important role in the persistence of European unemployment (see, e.g., Blanchard and
Jimeno 1995 and Ball 1996).
26
=
(j>i{xk,xi)
The
(l>i{x^i/xiY,
long-run technological
maximum
menu
i
e
{k,l},
technology by
is
Unitary specificity
(f)i{xk,xi) also
which captures
linear,
is
size
ratio.
depends on technology and
specialized with respect to the latter.
which each unit of capital
The
[0,1].
Because of constant returns the
tal/labor ratio. If a unit of capital, for example, works with
more
^G
[0,1),
immaterial, so an appropriate normalization allows us to identify a
embodied capital/labor
its
e
y"'{xk,xi) for production
possibilities of long-run factor substitution.
of production units
(j)i
is
strength of this effect
more
The presumption
labor,
it is
be
likely to
thus that the degree to
is
with the technology's labor intensity.
specific to labor increases
is
a function of the capi-
is
captured by the parameter
As an example, consider the
/i.
possibiUty of substituting generic machines for specifically trained workers. Capital specificity arises if
substituted for workers, the share
An
institutional
pay. If severance
labor/capital
Our
example
pay
is
when
arises
fixed in
of specific training in total capital investment
(pk
monetary terms,
presentation does not aim at
it
effectively
mechanisms
likely to
(Parameter Configuration) We
l'/2'
ing parameter configurations:
The upper-bound
technology choice
and labor
is
(i)
is
(i)
a<
1; (ii) T]k
=
rji
=
restrict
case.
which unitary
specificity does
form implies,
proportional to total labor use xi
may
/x
€
Assumption
rj.
depend on
{0, 1}.
why
effective specificity
(i.e.,
simplifies
(Hi) restricts the
1
or
0.
We
take
relative factor use, as our base
may depend on
(f>k{xk,xi)xk
We contrast
=
4>kXi), as
would
this with the case
factor proportions
not be independent of the capital/labor ratio either.
27
two values,
(ii)
for exzimple, that total capital specificity
cate our training and severance-pay examples above.
^''Another reason
(Hi)
to the follow-
an interior equilibrium. The elasticity-based distinction between cap-
in the unitary-specificity function (pi{xk,xi) to
is
our analysis
on the productivity parameter a guarantees that equilibrium with
Specifically, the functional
strength
proportional to the
not central to the results in this section, and assumption
value, for
<j)k{xk,xi)xk
and
r]> 0;
things by assuming that both factors have equal elasticity
first
4>k
and 2 with assumption r/2':
Assumption
the
legislated severance
be at work more generally. With this in mind, we
1
/x
makes
falls.
but focuses on selected cases that axe
full generality,
replace assumptions
parameter
from
capital specificity derives
are
ratio.'^'^
indicative of the
ital
As machines
the firm finances workers' relationship-specific training.
is
n
indi-
=
0,
that relative bargaining
where unitary
specificity does not
depend on
relative factor use.
Equilibrium with technology choice
How
is
equilibrium determined with technology choice? Suppose temporarily that any
point on the technology
that maximizes
its
menu were
Then each
available.
would
select the technology
factor income in Joint Production, subject to the other factor being
willing to participate. In other words, Xi units of factor
x^i
factor
= argmax
{wf{xk,xi)xi
s.t.
i
would choose
u;"j(xfc,x;)
>
p^j}
2
,
=
1,2,
(28)
x-,i>0
where wf{xk,xi) and w^^{xk,xi) are given by
As we
(8)- (9).
discuss below, optimization
together with equilibrium free entry determine the technology that
—
if
given the choice
— would
select
from the technological menu. The question
that technology be actually developed?
We
do not model
technological development and adoption. Instead,
if
there
is
unanimity
in all
new production
new production
we
rely
on a simple long-run
will
principle:
relationships about a single technology, then
new production
Since
are identical, they would select the
same technology and, according
all
relationships in our
model
to the "unanimity"
be developed.
principle, that technology will
mind, we define an
this in
is,
any detail the process of
in
that technology will be developed.
With
units
(interior) incomplete-contracts equilibrium with tech-
nology choice as a set of variables {xi, X2, C, E, E\, E2, Pi, P2, W^, W2, y°) that satisfy
technology-choice problems (28), the normalization xi
an
(interior) incomplete-contracts equilibrium.
with technology choice
As stated
which
in the
We
is
1,
as well as the conditions for
define an (interior) efficient equilibrium
same manner.
in proposition 13 below, there will still
specificity
=
be some parameter configurations for
balanced in equilibrium and other configurations for which one of the
factors appropriates the other
appendix shows that,
and experiences market segmentation.
in the first case, technology
is
Section 6.5 of the
determined in equilibrium by the joint
free-entry conditions of the two factors (the first-order conditions for (28) generally serving
to identify the constraints'
shadow
price). In the
second case, technology
is
determined by
the first-order condition of the appropriated factor:
Proposition 11 (Appropriation and Technology) Suppose
ated
(i.e.,
A,
>
that factor
i
is
0^ in an incomplete- contracts equilibrium with technology choice.
28
appropri-
Then
the
equilibrium choice of technology Xk/xi
determined exclusively by factor
is
i's
unconstrained
optimization problem maXx^i>o{Wi^{xk, xi)xi}, given equilibrium pk andpi.
The
Since
its
free-entry condition holds with
breaks even with
its
optimal technology and would
intuition behind proposition 11
equality, the appropriated factor
suffer
a
i
is
simple.
with any other technology. The other factor has therefore no choice but to
loss
accept factor
i's
preferred technology. "^^ Although different in that
equilibrium outcome, this result
is
akin to the idea in the property-rights literature that
who must make
control rights are often optimally deposited with the agent
specific investment (see, e.g.,
purely a market-
it is
Grossman and Hart 1986;
Dow
the largest
1993).
Before characterizing equilibrium with technology choice, we address the question of
existence and uniqueness:
Proposition
1'
(Existence and Uniqueness)
technology choice
exists,
is
and
unique,
An
satisfies
equilibrium with technology choice exists,
is
incomplete- contracts equilibrium with
C,Ei,Ui
>
0,
unique, and satisfies
z
=
An
1,2.
C*,E*,U* >
0,
efficient
—
i
1,2.
Exclusion and withdraujal
The problem
of appropriability can cause an inefficient technology to be chosen.
to see that, because
we have assumed
choice of technology has Xk/xi
=
1.
full
symmetry between the two
With incomplete
It is
simple
factors, the efficient
contracts, this capital/labor ratio
is
generally distorted:
Proposition 12 (Exclusion and Withdrawal) Suppose
anced
specificity
factor
i
and
the efficient technology Xk/xi
takes place, causing
</)j
>
(f)^^.
=
1.
the
economy
An
institutional shift against
initially
bal-
Define the "short-run" response (superscript "s.r.")
as the incomplete-contracts equilibrium outcome with fixed technology (xk/xi
"long-run" response (superscript
has
"l.r.")
=
\);
as the incomplete- contracts equilibrium
and
the
outcome
with technology choice.
(i)
If
n=
1,
then
xl-^
„l.r.
(ii)
If
ij,
=
0,
>
^
<
and
Eb,l
and
E^>Et:[-.
rf.s.r.
Et;l
then
„l.T.
±»
25 r
^Technically, "constraint qualification"
ated first-erder condition
is
„s.r.
<±i^
is
not satisfied for factor -i's optimization problem.
therefore not necessary.
29
The
associ-
Let factor
rameters
—
(capital, for concreteness) experience a detrimental shift in specificity pa-
i
i.e.,
a increase in
or a decrease
(/»^
short-run response with fixed technology
than
Prom
proposition
1
remains
technology will be chosen. In the base case
//
=
and the capital/labor
ratio xf^/xtj'
1,
also be
shown
underemployment of capital
to alleviate the
and
Et;[- are
lower
the long run, an
capital will be substituted for
The
under-employment
its
we know that the
fixed. In
labor leading to an inefficiently high capital/labor ratio x\-^/xb^j-.
of labor from Joint Production exacerbates
3,
£'?''
under-employment:
is
—
efficient
inefficient
(p^^.
partial "exclusion"
(Eb,^-
(£'''"
>
<
Et;l'
,
and can
Excluding
Ef'^)?^
labor helps reduce the net specificity of each unit of capital, and reduce appropriable rents.
By
/x
contrast,
=
0,
if
unitary specificity did not depend on relative factor use, as
then the opposite would happen. The capital/labor ratio would be
is
the case
when
ineflttciently low,
as capital "withdraws" from Joint Production in an attempt to capture a bigger piece of
quasi- rents per
The
we
own
unit.
rationale behind exclusion
and withdrawal
=
use the accounting identity y"
w'^Xk+wYxi together with
function in (28) for appropriated factor
w'^{xk,xi)xi
where Ai{xk,xi)
given by (13).
is
social point of view
term
— net
(i.e.,
=
1, it is
/x
=
0,
>
0.
(21) to rewrite the objective
as
[y"(xfc,a;/)
The
first
- p-,iX^i] -
Ai{xk,xi),
term expresses
i's
(29)
objective function from a
How
p-,i);
eff'ect
of changing factor proportions on net specificity
Excluding the other factor helps reduce net effective
by a problem of distorted capital/labor
is
had developed labor-market
is
specificity. If
ratio.
aspects of high unemployment in Europe.
oil
If
reduced, but replaced
This analysis of the technological response to rent appropriation can shed
a result of
the second
does the second term distort the resulting technology?
the opposite would hold. In both cases rent appropriation
ally considered
if
— captures the private distortion to that objective function
easy to see that the
given by dAi/dx^i
i
can be made clearer
based on the other factor's social shadow cost
eff'ective specificity
due to rent appropriation.
/x
=
in proposition 12
The
rise of
unemployment
light
in the 1970s
on some
is
gener-
shocks and of the productivity slowdown on economies that
institutions better
adapted to an era of rapid growth.
Wage
^®In fact, with our assumption of infinite elasticity of factor substitution, technology choice will cause
capital to be ot;er-employed
disappear for lower
compared
to the efficient outcome.
elasticities of substitution.
30
But
this result is not robust,
and would
resistance to adjustment caused an increase in the labor share of national incomes
contraction in employment. In the 1980s the labor share reversed
unemployment kept
sharply, but
its
and a
course and declined
Blanchard and Katz 1996). The labor
rising (see, e.g.,
share of value added in French manufacturing, for example, rose from 61 to 68 percent in
the 1970s, but then declined to 58 percent by the end of the 1980s.
One
plausible driving
phenomenon
is
a technological response to appropriability characterized
by labor exclusion: As capital
is
substituted for labor, the labor share declines while un-
force behind this
employment
Looking again at the example of France, one finds evidence of strong
rises.
capital/labor substitution. Between 1970 and 1990, the capital/labor ratio in French
man-
ufacturing increased by 122 percent versus 88 percent in the US. Normalized by the capital
labor ratio in the trade sector, the increase was 25 percent in France versus 8 percent in
US."
the
Balanced- specificity region
As does
institutional development, the introduction of technologies with
characteristics
run.
The
may
help balance specificity and eUminate market segmentation in the long
following proposition characterizes the region in the space of specificity parameters
i,4>k->4>i) ill
which
eflFective specificity is
balanced with technology choice.
Proposition 13 (Balanced-Specificity Region) For
rium with technology
ters
C
{(f)f.^ (f>i)
[0, l)'^
(ii)
7/77
>
choice, define the
for which equilibrium
as the set of parameters
The
(i)
new factor-intensity
efficient set
£
is
The balanced- specificity
1,
then £
C B C
{(l)f.,(f)i)
the line
(pi^
£ C
"efficient" set
is efficient;
=
the incomplete- contracts equilib-
and define
for which
A=
the
m
as the set of
[0, l)'^
parame-
"balanced-specificity" set
B
equilibrium.
(f>i;
set includes, but is not generally equal to, the efficient set:
[0,1)2; if
rj
<
1,
then
£
=
B\^^-^
C
B\^^q
C
[0,1)2
^^f^^^^
a^v
denotes strict inclusion).
Statement
is
(z)
of the proposition identifies the efficient set
intuitive since
From
proposition
we have assumed everything
2,
we know that with
else to
£ with the
^^ Another piece of evidence
(})f.
=
(f)i,
which
be symmetric for the two factors.
fixed technology the balanced-specificity set
also correspond to a line. In the long run, technology choice can
correlation observed between
line
expand the
would
possibilities of
on labor shares that is consistent with the exclusion effect is the strong negative
wage premia and the labor share of value added in US industry (see Krueger
and Summers 1988, and Katz and Summers
the eissociated low labor share
may be
1989). If part of the
wage premium
reflects specific quasi-rents,
the result of a labor exclusion response to rent appropriation.
31
balanced specificity and turn the line into a broader cone, illustrated in figure
in
B
the balanced-specificity set
(ii),
broader than the
with technology choice can generally cover a region
The reason
efficient line £.
As stated
3.^^
is
A
that
can be reduced to zero through the
adoption of technologies with suboptimal relative factor intensities. Technology choice
therefore another reason
why
is
analyzing the economy near a balanced-specificity point can
be reasonable.
However, there are limits to the degree to which factor substitution allows
specificity to
be balanced in equilibrium. Going back to the objective function
(29), using factor substi-
tution to reduce rent appropriation Aj
term y"(xfc,X()
As
factor substitution
is
on to
relied
the resulting marginal inefficiency
tion.
B
For this reason the set
is
does not generally cover the
0.
0.
Thus,
it is
more
difficult
with factor exclusion than
the partial-equihbrium
offset
equihbrium
effect
straightforward to see that dAi/dpi
>
the appropriated factor, the general-equihbrium effect of
if i is
exclusion, which causes pi to rise and p^i to
is
is
Taking into account the general-equilibrium variables that determine net
and dAi/dp^i <
and p^i
parameter space. Market
while they reinforce the effect of withdrawal
1,
effective specificity Ai{xk,xi;pk,pi) in (13),
partial
a point where
infinite elasticity of factor substitution.
when ^ =
rebalancing effect of exclusion
=
full
because general-equilibrium forces
is
may come
—p-,iX-,i.
greater than the marginal reduction in appropria-
a sense in which balancing specificity
with withdrawal. This
when ^
costly for the efficiency
offset appropriation, there
is
segmentation can arise even with an
There
is
=
when ^
1
.
The
fall,
is
to increase Aj and partly offset
its
general equihbrium effect of withdrawal on pi
the opposite, and helps reduce Aj further
when
/z
=
0.
Thus the former
results
in greater distortions in factor intensity than the latter.
A
prices
measure of the strength of the general equilibrium
is
how low
the elasticity
the proposition states,
efficient line £;
when
but when
effect eliminates
77
<
of factor supplies
t]
>
r/
1,
1,
the appropriating factor
-iz
77
region
<
1,
B
coincides with £.
is
B
The strong
is
on relative
/x
=
1.
As
greater than the
general-equilibrium
specificity outside the efficient line.
In fact
the exclusion effect actually worsens segmentation of
outside the efficient
notation of proposition 12. This
Consider the base case
the balanced-specificity region
any possibility of balancing
one can show that, in the case
is.^^
effect of exclusion
line, i.e.
wb^^-
—
p'j,j
because, by (20), segmentation
^*
Figure 3 was generated with rj = 1.5 and ^ = 1.
^^More generally, if Tjk ^ fli, the relevant measure of the strength
low a weighted average of the two factors' supply elasticities is.
32
is
>
wt;l'
—
pf;f in the
equal to A/x-,j, which
of the general-equilibrium effect
is
how
9*2
0.0
—
^^
0.1
'
'
0.2
0.3
0.4
T
T
T
0.5
1
1
0.6
1
0.7
1
1
O.B
0.9
1.0
1
1
1
xV
\v
Fac tor 2 Segmented
y
X\ \v
1
\.
X
^N,
\\ \
\
/
~~-~-..____
C
•
\
\
1
1
Factor
\
\
0)
1
-
1
1
B)
3
\\
(D
r^
\
CO
"
\
SI
Segmented
to
V
\
3
o
\
o'
D
M
n
a.
i
/
X/
Specificity
\
\
can
when a strong
rise
(i.e.,
reduction of
x-,i)
general-equilibrium effect necessitates a great degree of exclusion
to decrease
A. Thus, exclusion of the appropriating factor through
technology choice not only leads to greater under-employment for that factor, but
may
also
lead to greater factor segmentation.
Conclusion
5
The prevalence
of specificity in economic relationships
suspect for a wide range of economic
ills.
In this paper
makes rent appropriation a prime
we have
tried to provide a simple,
synthetic characterization of the multidimensional macroeconomic problem
Why
do economies waste unemployed resources during recessions?
voluntary unemployment and labor market segmentation at
all?
Why
it
gives rise to.
Why
is
there in-
do some economies
Why do countries build social institutions that
are later perceived as obstacles to flexible adjustment? Why do some countries seem stuck
with a highly outdated productive structure? Why is the massive destruction of reforming
countries' old productive systems not matched by immediate and significant creation? Why
"over-heat" at even modest levels of growth?
are
methods of production
(e.g.,
capital/labor ratios) so different across economies that are,
otherwise, at a similar stage of development?
often
fail
It is
Why
do poor countries with cheap labor so
to attract capital and grow?
certainly not inconceivable that part of the answer to those apparently disconnected
questions could be traced back to appropriable quasi-rents. As this paper argues, each of
the phenomena those questions touch upon
may
reflect
a different aspect of the economy's
general-equihbrium response to widespread opportunism.
33
Appendix
6
Construction of Equilibrium in Section 2
6.1
This section derives a constructive characterization of incomplete-contracts and
equilibria that will prove useful in
what
follows.
An
incomplete-contracts equilibrium
constructed in the following manner. First use equations
Pi{E)
that give pi
values Pi(0)
=
=
=
Pi{E) in equilibrium.
and pi{+oo)
=
+oo.
{xiE)^/""
Pi{E)
Now
is
,
i
efficient
=
(3)
and
is
(6) to define functions
l,2,
(30)
continuous, strictly increasing, and takes
free-entry condition (14), which
is
equivalent to
can be written as
(12),
y"
<
Given that
> max {(1 + 4>i)pi{E)xi +
(j)j
properties of Pi{E):
f{+oo)
=
-l-oo.
<
1,
it
Since y"
j
is
=
1,2,
it
is
(1
-
<t>^^)p^i{E)x-.i}
clear that the function
=
f{E).
f{E)
(31)
inherits the
above
—
and
continuous, strictly increasing, and takes values /(O)
>
0, this
impUes that free-entry condition
yields a unique positive value of E. It
is
(31) taken with equality
easy to check that the other equihbrium variables
(C, Ei,E2,pi,P2,Wi,W2,y°) are determined uniquely as a function of
E from the remaining
equilibrium conditions.
Free-entry condition (14) can also be thought of as relating employment
net specificity
— a relation that
will
prove useful.
The
function
^(A)
E=
^(A)
to
implicitly defined
is
by
y""
It is
continuous and strictly decreasing.
An
efficient equilibrium
figuration of
To
= Pi{E)xi + p2iE)x2 + A.
{(pi,<f>2)
see this, one can
corresponds to an incomplete-contracts equihbrium with a con-
that yields
first easily
A =
(which includes the configuration
check that the definition of an
sponds to that of an incomplete-contracts equilibrium
^(A)
defined above takes value
E* when
A=
34
0.
if
A = 0.
Conversely,
efficient
(pi
=
4>2
=
0).
equilibrium corre-
In particular, the function
A =
is
necessary for an
incomplete-contracts equilibrium to be efficient because, since
E{A)
is
strictly decreasing,
Proofs of Propositions in Section 2
6.2
Proof of proposition
The
1:
existence and uniqueness of an incomplete-contracts equi-
librium was shown by construction in section
6.1.
It
was
also
shown that an
efficient
=
(among
equilibrium corresponds to an incomplete-contracts equilibrium with
(pi
=
(f)2
other possible ((/»i,^2)-configurations), which therefore guarantees existence and uniqueness. It remains to
=
<j>i=<l>2
First,
be shown that C,Ei,Ui,>
0, i
=
1,2
{C*,E*,Ul >
follows
by setting
0).
we show that
C >
which, by
0, for
(2), it is sufficient to
show that
E >
E°.
Define the function
g{E)=x\^^''''E^I^' +x\^^''^E^I^-\-mB^[x\^^''''E^I^\x\^^''^^E^I'^^].
One can
E.
show that g{E) > f{E)
easily
Since ze
employment
assumption
is
the solution to y"
1 implies
for
which the
= xiE >
= 1 — Ei >
minimum y"
follows
from
we show
0,
E>
0,
g{zE) and equilibrium
<
E.
which was shown
that Zy in assumption
efficient equilibrium exhibits zero
To
the factors.
f{E), we must have ze
for
for all
Thus E° < ze
in
E° < E.
Second, Ei
show that Ui
=
0,
=
defined in assumption 1 as the solution to y"
is
>
and g'{E),f'{E)
(defined in (31))
1 is
in section 6.1.
the
minimum
Autarky employment {Ei
=
Third, to
value of y"
1) for
one of
see this, note that, by substituting (30) in (10) (taken with equality), the
which E*
=
1 is
.(:.(^-"Zy
is
simply the
1 implies
E* <
minimum
1.
of the above expression for
i
=
1,2.
Thus y" <
Since proposition 3 (proved below) states that Ei
Zy in
<
assumption
E*, this implies
Ei<l.a
Proof of proposition
equilibrium
is
that this
2:
is efficient iff
is
The
A=
first
part of the proposition
— was proved
— that an incomplete-contracts
in section 6.1.
What we
still
need to show
equivalent to parameter condition (19). Solving (10) and (18) simultaneously
35
for (pi,P2),
If
we
(3)),
we
get
replace this expression for pi in (6) and use the fact that Ei/xi
we obtain
that E'{A)
<
this implies that
—
and E(0)
equilibrium, in which
Ei
<
A>
E^,
by proposition
i
=
5:
Given
dW
—
=y
By
in the
„
-D'{y^)
main
— pi) +
A2
{'W2
proposition 4 and Ai,A2
>
0).
Proof of proposition
7:
(3),
text.
[f - piXi - P2X2)
By
inefhcient equiUbrium (by proposition 2).
[Ai (to"
and
C
and y°
yields
-pixi -P2X2\
(14) taken with equality, the first expression
—D'{y°)
in equilibrium,
d
1,2.
—=
E{A)
E = E{A) < E{0) — E*. By
must have
2,
Differentiating (23) with respect to
6:
equation
This imphes that an inefficient incomplete-contracts
E*.
Proofs of propositions 4 and
Proof of proposition
E=
Recall from section 6.1 that
3:
£'2/2:2 (see
D
condition (19) in the proposition.
Proof of proposition
=
— P2)], which
is
is
.
equal to A, which
(16),
is
positive in
the second expression
is
an
equal to
negative in an inefficient equilibrium (by
Taking (21) into account, the equilibrium entry and exit con-
ditions with subsidies are
y"
y°
where
-'i
(7°
+ a° = pixi + P2X2 + A^i A,
denotes the appropriating factor. Substituting the
tions ((10) with equality
and
+ cr" = pixi + P2X2 + A;
for their
and
(17)) for
efficient
entry and exit condi-
y" and y° in the formulae above, and replacing
proposed expressions, transforms the equiUbrium conditions into
=
=
which are obviously
(pi
(Pl
- pI)xi + {p2- P*2)X2 + (A -
-p\)xi
satisfied iov
+
(p2 -P*2)x2
E = E*. D
36
+
(A^iA
-
A*),
A^iA*),
cr"
6.3
Proofs of Propositions in Section 3
Proof of proposition
Prom condition
8:
we
(19) for efficiency,
y"*":
solve for
>0.
To determine which
factor
— ^iXipi{E). By
(j>kXkPk{E)
segmented, rewrite (13) in terms of functions (30):
is
differentiating this expression at a point
where
=
Ajt
0,
A^ =
we
get
dAi
dE
which
is
negative given that
rik
\
>
=
when y" <
we
y"**,
>
get Afc
=
f{E)
(i.e.,
<
(i.e.,
Proof of proposition
9:
Suppose that
Then
and
and
the capital market
y"' y^ y"''
— (1 + (pi)piXi H
y"
is
E
it is
E'
^"
at the
unique
segmented by proposition
is
and that
-
=
segmented) when y"
y"**.
D
the appropriated factor.
is
i
>
4)
Substituting functions (30)
i.
and y", we get
dE
(f)^i)p-,ix-
for the efficient equilibrium is
Comparing those two equations,
and only
(1
and that A^
E
y"
The corresponding equation
obtained by setting
(j)i
=
(p-^i
=
0.
clear that
^ dE*/E ^ E ^ dE/E
y"'
dy'^/y^
dy'^jy^
if
—p\xi
+
—
p*-^iX^i
which, after a few algebraic steps,
XV-^i
in section 6.1),
totally differentiating with respect to
dy"
(
an increasing function of y" (which
is
free-entry condition (12) holds with equality for factor
for the pj's
if
£^
the labor market
Afc
y"*";
(pkXkPkiE),
Vl.
Noting that
rji.
follows immediately from equation y"
value for y"
V^A:
Afc=0
)
[P*i
Vi/
-
(1
-
(f>^i)P^i]
^^i
> —(1 + (l>i)piXi
is
H
(1
-
(f)^i)p^iX-,i,
equivalent to
>—[(! + (t>i)PiXi +
(1
-
(t>-.i)p-.iX-.i
- p*Xi - p* jX^i] =
Vi
(32)
The right-hand
side of the above inequality
is
37
zero, because
it
is
equal to the difference
0.
between the right-hand sides of the
(10).
3)
The
sign of the left-hand side
>
imphes p*j
is
— then
r/i,
segmented, then
rj^i
77-,,
is
>
rji
Proof of proposition
10:
(i)
— 1/rii,
>
since £'*j
appropriated factor
if
< ^^;
and
E^i (proposition
—
capital
is
i
and ^^'
inequality (32) holds,
labor
i.e.,
is
on the contrary,
if,
> ^^.
and ^^*
Proof of the Proposition
6.4
efficient free-entry conditions, (14)
the sign of l/rj^i
Thus,
(30).
<
segmented
capital
by
p-,j
and
inefficient
in Section 4.1
Factor
i'
aggregate income (27) can be written as a function
of the other factor's net specificity A^:
Wi{A^i)
taking into account
^i
>
<
and E'
maximized
factor
i.
for
By
0, it is clear
A-,j
<
when
0,
> W^{A^i)
—
A^^
AL,j of
=
line in
(f)^ip^i
(^ {\A^i\))
parameter space
i
if
employed
=
in Joint Production,
it is
for
in section 6.1.
any A^j
<
Since
So Wi{A^i)
0.
is
net effective specificity in favor of
i.e.,
the latter
is
proposition 4 that
negative. If A-.^
the accounting identity y"
=
u;"x,
>
-I-
is
-
(f (lA^il))
<i,ipi
=
fix A-,i
(33)
Al^j.
>
again because p^
0,
increasing with
(f)^i
is
,
we
write
always increasing with A-,i when the latter
wf =
which
is
6.5
Mathematical Appendix to Section 4.2
This appendix provides a proof for propositions
is
pi f£'(|A-,j|)j
<
,
j
y"
(
always increasing with
(pi).
which increases with
=
that w^^
— p-,, ^ A^
(
(
|
j
|
p^i.
) j
1)
Using
x^^ j /xi
qualification condition
is
satisfied for this
problem
and
1',
in that order.
38
(28) for factors
—
,
non-negative.
11, 12, 13,
and optimization problem
If
A-,j
Equilibrium
with technology choice involves an additional endogenous variable Xk/xi (equilibrium
being normalized to
is
For a unit
0.
and decreasing with
we know by proposition 4
to" jX-,j
—
and E'
income wf
ex-post
wf = pi = pi (E (|A-,j|)
0,
Xi,
Autarky, ex-post income pi
we show that
easy to see from (33),
we know by
x-,i
we
in
at the efficient value of A-,i
A-,i (which,
and E{.)
,
definition (13),
For a unit of factor
employed
[E{\A^i\))
definitions of pj(.)
that Wi{0)
a non-negative value
which defines a
maximized
and the
(3), (21),
A^i
(ii)
= m3^{A^i,0}xiE {\A-.i\) +pi
i.e.,
i
w^^{xk,xi)
=
>
k,l. If
xi
the constraint
p-.i for
some
feasible
— then the following
value of x^i
"^p-^'>
ox^i
We
first-order condition
+Q.^-^=o
ai«i-p^i)=0,
and
ox^i
divide the parameter space
sponds to parameter configurations
{4)f.,(f)i)
for
necessary:
is
€
[0,1) into three sets:
which factor
is
B
Suppose
11:
{(j)f.,(pi)
=
i
A,
(34)
k,l, corre-
>
0) in the
0).
€ Ai. Proposition 4 shows that, with the
equilibrium technology Xk/xi, factor
z's
market clears and factor
This means that the constraint
>
p-,i
u;"^
(i.e.,
0.
corresponds to parameters for
(A =
characterized by balanced specificity
Proof of Proposition
Ai,
appropriated
i is
incomplete-contracts equilibrium with technology choice;
which equilibrium
some a^ >
for
to factor
z's
-iz's
market
is
segmented.
technology-choice problem (28)
is
not binding in equilibrium. First-order condition (34) becomes
djw^Xj)
dx^i
^
~
1
a
2
2
T / Xi
^"^^
~
x^-/^
Pi
V^ j
-
/.
(^1
taking (8)-(9) and assumption 4 into account.
-
It
..
(1
.^
- /^)'^-i
/ X-
[—
N^
)
)
P-'
=
(35)
0,
determines technology Xk/xi given equi-
librium pk and pi
Is this
i's
market
technology consistent with factor
clears
{wf
—
=
pi
-li^s
technology choice problem? Since factor
0) at this (unconstrained)
optimum
technology, no other
technology can yield a positive value for lo"— p^. Therefore constraint qualification for factor
-li's
problem does not hold, and the associated
We
first-order conditions are not necessary.
can now determine equihbrium quantities (and prices) in regions Ak^ Ak^ and B.
Suppose
section 2
{(f)k,<l>i)
€ At. Given technology, equihbrium employment
— by appropriated factor
(taken with equality) by
E
z's
after taking
is
determined
— as
in
free-entry condition. Multiplying each side of (14)
assumption 4 into account, and using
(3)
and
(6),
yields
f
iE.
. E^) =
Since (3) implies Xi/x^i
(l
=
. ^. (^)") Er'- .
(l
- ^,
(^)') <-".
Ei/E^i, (35) and (36) can be solved simultaneously to yield
equilibrium quantities in region Af.
if/x
=
0,
,36,
Ei=(^-^]
2i+^J
and
'^"^
39
E^r
^^'
=
V^i-"*-
Suppose now that
G B. The two
{4)k,<l>i)
factors' free-entry conditions hold
then with
equaUty (and are equivalent). They can be used to determine equilibrium quantities Ek
and
El. Multiplying both sides of the balanced-specificity condition (pkPk^k
and taking
(3), (6),
fi/E„=*,
=
4>iPi^i
by E,
and assumption 4 into account, we get
where
v,
= | <*-''*')'"^'
I
'f
W-
and
?^
1
+
- 2;. ^
1/,
0.
otherwise,
1,
(38)
for
i
=
k,l.^^
We
with equahty and
can use this expression to solve
A = 0),
for
Ei in free-entry condition (14) (taken
again after multiplying both sides by
E and taking
(3), (6),
and
assumption 4 into account:
Because the constraints to technology choice problem (28) are binding
in B, the as-
sociated first-order conditions (34) determine the constraints' shadow prices Oj.
first-order conditions to hold,
in B,
it is suflficient
(35) for
we need
to check that a^
by continuity to check a^
>
>
on that
d{wfxi)/dx^i and a similarly derived expression
Since the line
0.
line.
for
To do
so,
(p^
=
For the
is
<f>i
always
we use expression
dw^^/dx^i:
+ (i-(i-M)0,(|-) 1p.£;-+^^., (£;-)%.,
Since both factors are symmetric
under symmetry (by (14) with
when
A = 0)
(p^
=
^i, i* is
Proof of proposition
12:
— using a/2 =
pi
=
p^i
— that
dx-,i
in that case. It follows immediately
easy to see
dx-,i
from (34) that aj
Suppose parameters
In the short run with fixed technology Ek/Ei
=
>
0.
shift against factor
1, (6)
and
i
so that
(14) (with equality)
<^j
>
(^-,j.
determine
equilibrium quantities:
^r'E^Note that
if 1
+ I/t/ - 2/x = 0,
then
{4)^.,
0, )
=
G
B
[^^^-^].
iff
40
<^j.
=
i^,
.
This
justifies
(40)
the value
i/)i
=
1 in
that case.
The proof of the
and with
proposition follows directly from comparing (40) with (37)
(38)-(39)
if
(^k^^i)
€
if {^ki^^i)
Ai,
eB.U
We now characterize the boundaries that delimit the different regions in parameter
space. We start by determining all the "smooth" boundaries — i.e., boundaries at which
equilibrium variables are continuous functions of the parameters {^k,^i)- Note
any point that smoothly separates Ak and Ai must be included
factor- market segmentation
At any point
and
B
smooth boundaries that separate region
attention to
We
would involve a discontinuity).
in
B
(otherwise the
can therefore
from regions Ai,
=
i
that
first
flip in
restrict
our
k,l.
{4>k,4>i)
along such a boundary, equilibrium must satisfy equations (37)
(39) simultaneously.
Equating Ei/E^i as determined by each of those two equations,
a smooth boundary must satisfy
i_
(j)^i
=
where
h^{(j)^J(t)i),
= —-^^
hi{z)
(?l>t
=
=
(/)_,,
origin
and
0).
+ 1/r/ — 2/i ^
and
(otherwise
it
In the space of parameters {4>k,^i)
€
7^
</)j(?!>_,j
1
and must remain on the
1
^10(2)
1
must
-3-,
+2
(41)
1+1
satisfy the continuous extension
[0, 1),
side of the 45 degree line
z^+1
1
=
+1
Z n-i
as long as
1
—
ij-l
Z
such a boundary starts at the
where
>
(p^
Points between
(j)^^.
the 45 degree line and the boundary are in B, and points between the boundary and the
<^j-axis are in
in Ai.) It
A-
(If this
were not
so,
then a point such as
easy to check that this configuration holds
is
direct consequence of the fact that hn{z)
hold
ii fi
=
and
1
<
r/
G
(in this case hi{z)
[0, 1) iff
G
[0, 1) iff
<
z
(0j,(?!)_,j)
if /z
=
<
1,
z
>
1).
=
0, or if
(1,0)
=
/u
1
in this case);
By symmetry,
would not be
and
77
>
(a
and does not
the set A^i
is
a mirror image of Ai.
Thus,
i
=
k,l,
if /x
and
is
=
0,
or
/x
=
1
and
t/
flanked by the sets
>
0,
the set
B
Ak and At on
lies
each
boundaries exist (other than at the origin). The set
and the
sets
Ai to the space between that
Proof of proposition
Statement
13:
essary condition for efficiency
(37),
it is
clear that
Ek/Ei
=
(i):
side. If
B
and the
^=
only
if
(pi
=
Statement
(ii)
Thus the
efficient set
and
77
<
0,
for
no smooth
line,
<^j-axis.
Since the two factors are symmetric, a nec-
4>k-
But
(pi
=
(pk is
=
£ corresponds
1.
also
for efficiency, because, given the efficient technology, proposition 2
quantities are efficient.
1
corresponds to the 45 degree
a symmetric technology Xk/xi
is
1
line
between the two boundaries (41)
Looking at (39) and
a
sufficient condition
shows that equilibrium
to the line
cpi
=
(pk-
follows immediately from the above characterization of the different
41
regions.
D
Proof of proposition
Existence of an incomplete-contracts equilibrium with tech-
1':
nology choice was shown above by construction. Uniqueness follows from
determination of regions Ak, Ai, and
because the two sets
lie
on opposite
the latter contains the 45 degree
on
(37) for region
We
Ai and on
(a point in region
Ak cannot
sides of the 45 degree line;
and smooth boundaries
line,
and (a) the unique determination
B
>
(41) Eire
and
(1
(39).
(2)-(3);
Ui
=
1
and Ei
—
+ 0-,z)/(l + ipJ^
The above
efficient
)
follows
follows
from a
from a
>
<
cannot be greater than
existence, uniqueness,
(pi
=
if
B
because
they
exist);
>
(pk-
0,
i
3),
=
C >
1
in equations (37)
and
42
Because we
follows
from
<
1)
(39) (noting that
2).
and interior-equilibrium properties
^
k,l.
in equations (37) (recalling that 0^
equilibrium with technology choice, since
rameter configuration
in
Ai
(39) for region B).
>
>
Ei
unique
in region
of equilibrium variables in each of those regions (based
turn to the interior-equihbrium properties C,Ei,Ui
hy
be
and cannot be
have assumed that there are no pre-existing units (assumption
Ei
also
the unique
(i)
it
also apply to
an
simply corresponds to the special pa-
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