Testing the Efficiency of Employment Contracts
Author(s): James N. Brown and Orley Ashenfelter
Source: Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor
Conference (Jun., 1986), pp. S40-S87
Published by: The University of Chicago Press
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Testing the Efficiency of
Employment Contracts
James N. Brown
State University of New York at Stony Brook
Orley Ashenfelter
Princeton University
The recent literature on employment contracts emphasizes that it is
in the interests of the parties to produce institutional arrangements
that lead to employment contracts that we have termed "strongly
efficient." Strong efficiency implies that employment is set so as to
equate the marginal revenue product of workers to their alternative
wage. It follows that employment in such contracts fluctuates with
the determinants of a worker's marginal revenue product and with
the worker's alternative wage, but not with the observed contract
wage. We have examined two kinds of evidence to test the strong
efficiency hypothesis. Laboratory experiments by Siegel et al. indicate
that this hypothesis is strongly confirmed when the bargaining
parties are required to agree on price and quantity simultaneously
and is strongly rejected when the parties are required to bargain by a
system of price leadership. In our field data on the printing trades,
we find no convincing evidence of strong efficiency. We have also
examined the evidence in support of what we have called the "weak
efficiency hypothesis." According to this hypothesis, both the contract
wage and the alternative wage determine employment. We
have found only mixed support for this hypothesis because our measures
of the alternative wage available to workers are frequently
positively related to employment, precisely the contrary to the hypothesized
direction of this effect in a weakly efficient contract.
We are indebted to the Hoover Institution and to the Industrial Relations Section at
Princeton University for financial support of this project. We are also indebted to
Armen Alchian, David Card, Robert Hall, Oliver Hart, Edward Lazear, Andrew Oswald,
John Pencavel, and Robert Solow for many useful suggestions. Any remaining
errors are our own.
journall of Political Economy, 1986, vol. 94, no. 3, pt. 2]
?9 1986 by The University of Chicago. All rights reserved. 0022-3808/86/9432-0002$0 1.50
S40
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EMPLOYMENT CONTRACTS S41
I. Introduction
In recent years there has been a rebirth of interest in the idiosyncratic
nature of employment and wage bargains. The belated recognition of
the importance of specific human capital has emphasized that the
parties to these bargains enter them with skills or resources whose
values either are, or will afterward become, unique to a particular
bargaining partnership. This raises the old problem of determining
the wage and employment bargain that will be struck under bilateral
monopoly. A rich variety of theoretical models have now been developed
to describe labor contracts in the presence of bilateral monopoly.
As yet, however, little empirical work based on these models has
appeared. It seems an appropriate time, therefore, to begin the process
of laying out the methods by which these models might be tested
and their empirical relevance assessed.
The early theoretical analyses of bilateral monopoly date to
Edgeworth (1881), Marshall (1890), Cournot (1897), Pareto (1909),
Pigou (1920), and Bowley (1928). According to the prediction of
Cournot and Bowley, the typical case will involve bargainers of unequal
"strength," and one of these bargainers will be able to dictate
the price, while the other will establish the quantity traded. This leads
to the simple monopoly model of wage and employment determination
proposed by Dunlop (1944), which, of course, does not predict a
Pareto-efficient level of employment.
Empirical models inspired by the Cournot-Bowley-Dunlop setup
have been applied to labor market data by several authors, including
Farber (1978) for U.S. coal mining, Dertouzos and Pencavel (1981)
for U.S. printing trades, and Carruth and Oswald (1985) for British
coal mining. The assumed accuracy of this monopoly model also
underpins a number of analyses of union behavior, including Lewis's
(1963) study of the effect of unions on employment and Rees's (1963)
and more recently Freeman and Medoff's (1984) estimates of the
"welfare costs" of trade union wage and employment "distortions."
The essence of these models is that workers and employers end up
reducing the total amount of rents available to themselves in their
efforts to divide these rents.
The simple monopoly model implies that there are unexploited
"potential" gains from trade available to both parties. In contrast, an
alternative model inspired by Edgeworth and Pareto leaves the transacted
price indeterminate but predicts the quantity transacted to be at
its Pareto-efficient level. This leads to the model of employment determination
suggested by Fellner (1949) but with the wage rate determined
by other unspecified factors. Empirical studies inspired by the
Edgeworth-Pareto-Fellner setup have been carried out by de Menil
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S42 JOURNAL OF POLITICAL ECONOMY
(1968, 197 1) and Svejnar (in press). The essential idea of these models
is that bargaining over all factors that are not in fixed supply should
lead to the Pareto-efficient employment of all factors. Consequently,
there are no trade union "distortions" or "welfare costs."
These early empirical models did not carefully specify the information
about technology, costs, and demand that each party carried to
the negotiating table. More recent research on employment contracts
explores the possibility that incomplete information may prevent the
parties from reaching otherwise Pareto-efficient employment levels.
In the research surveyed by Hart (1983), for example, workers have
incomplete information about a firm's product demand. Since it is
never in the interest of the firm to reveal states of rising demand and
always in the interest of the firm to reveal states of falling demand, it
is hypothesized that no institutional structure in which all available
information is credibly shared by the parties can be established. The
problems thus created are mitigated, however, by contracts in which
employment is reduced below its otherwise Pareto-efficient level in
bad times, with the reduction in employment providing the credible
signal that it is mutually profitable for wages to be reduced.'
Hall and Lazear (1984) consider a simplified case in which workers
have incomplete information about product demand and firms have
incomplete information about workers' alternatives. In their analysis,
no single institutional setup will lead to Pareto-efficient employment
without excessive monitoring or information-gathering costs. Hall
and Lazear conclude that Pareto-inefficient separations are a natural
consequence of the presence of such costs in "free" labor markets.
In contrast to these results on "inefficient" contracts in the presence
of monitoring costs, an important conclusion to emerge from the
recent literature on "fully" Pareto-efficient bilateral contracts is that
employment should fluctuate only with the alternative wage available
to the workers who are a party to the bargain, and not with the
contract wage. When workers are risk neutral, this result occurs because
the opportunity cost of a worker's time is the alternative wage,
and both parties agree to set employment such that the marginal
product of workers is equated with their opportunity cost. When
workers are risk averse, this result can still occur because it is then in
the interests of the workers collectively to establish a scheme for unemployment
benefits that makes it profitable for workers collectively
to behave as if they were risk neutral. Finally, when workers as a
group cannot be characterized as maximizing expected utility, it will
' Put differently, in the presence of asymmetric information, optimal contracts
amount to an enforced relationship betwen wages and employment. This general idea
has recently been applied to the question of strikes by Hayes (1984) and was originally
spelled out by Hall and Lilien (1979).
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EMPLOYMENT CONTRACTS S43
then be optimal for the parties to engage a risk-neutral third party,
perhaps an insurance company or the firm's shareholders, and, barring
market imperfections, it will again be mutually profitable for
employment to fluctuate only with the alternative, as opposed to the
contract, wage.
It is this proposition that suggests a basis for our test of the efficient
contracting hypothesis. To be concrete we shall call the hypothesis
that the marginal revenue product of employment is determined only
by the alternative wage the strong efficiency hypothesis. Rejection of this
hypothesis implies that some obstacle impedes the establishment of an
employment relationship that is first-best Pareto efficient. Of course,
by itself, rejection of this hypothesis has no immediate normative
implications because the precise nature of the impediment preventing
efficiency has not been specified. Still, the rejection of this hypothesis
should lead to a search for the nature of these impediments and their
cause.
At a minimum, however, it is clear that, in any efficient bilateral
contract, the alternative wage rate must determine, at least in part, the
marginal revenue product of employment. If the alternative wage
rate has no role to play in the determination of employment, it is
apparent that, with the kind of data actually available, the simple
monopoly and Pareto efficiency hypotheses are empirically indistinguishable.
It is therefore worth knowing whether the available evidence
supports the hypothesis that the alternative wage plays at least
some role in the determination of employment. To be concrete, we
shall call this hypothesis the weak efficiency hypothesis. Our purpose in
this paper is to set out a variety of methods for assessing the empirical
relevance of these weak and strong efficiency hypotheses.
Our motivation for this analysis is twofold. First, a considerable
amount of policy-oriented research has assumed the empirical relevance
of the monopoly model of employment determination. Measures
of the welfare cost of trade unions and accusations of worker
overmanning and featherbedding all rest on the assumed relevance
of the simple monopoly model. If employment contracts are efficient,
however, unions merely generate transfers to workers from those
who earn rents from factors in fixed supply. From this viewpoint,
featherbedding may simply be the method by which the employment
contract is enforced and employers are kept from reneging, ex post,
on efficient bargains. In the simple monopoly model, an increase in
the bargaining power of workers leads to a higher wage rate but a
lower employment level as firms move up their demand curves. As
McDonald and Solow (1981) observe, however, in efficient contracts
we should generally expect an increase in the bargaining power of
workers to lead to a higher wage and at least as great a level of
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S44 JOURNAL OF POLITICAL ECONOMY
employment. Policies to weaken trade union and worker power in the
first case would lead to increased employment, whereas in the second
they would merely redistribute income from workers to capitalists
and perhaps decrease employment as well.
Second, an extensive body of empirical work in labor demand and
labor supply treats the current wage rate as the relevant measure of
the price of workers' time. If contracts are efficient and marginal
revenue products are determined either independently of, or only
partially by, the contract wage, however, all this work may be called
into question.2 Given this fact, we think it is especially important to
know whether the data warrant the role typically given to contract
wages in models of employment determination.
Our appraisal of the evidence on efficient employment contracts
makes use of two different types of data. We begin by discussing the
results of laboratory bargaining experiments on bilateral monopoly
conducted by Siegel and Fouraker (1960) and Fouraker, Siegel, and
Harnett (1961) some 25 years ago. We then turn to a detailed analysis
of macroeconomic field data on employment and wage rates in the
printing trades. Our interest in the printing industry stems from the
presence of (a) strong unions, (b) considerable rents due to the precipitously
increasing returns to scale already documented, and (c)
historical allegations of featherbedding in this industry.
II. Some Evidence from Experimental Data
Although our primary interest lies in explaining observed "field" data
on employment, we think that laboratory bargaining experiments
provide some insights that may be helpful in the interpretation of our
nonexperimental data, where the identification of supply and demand
parameters becomes entangled with the identification of different
behavioral hypotheses. In the bargaining experiments conducted
by Siegel et al., buyers and sellers were given profit tables listing the
net monetary gain associated with each possible price and quantity pair
they might agree on. For the buyer, profits were determined by a
linear average revenue schedule,
AR = a - bQ, (1)
which gave the price per unit at which the buyer could resell (to the
experimenter) as many units of the commodity as he purchased from
2 One might argue, e.g., that the small labor supply elasticities typically estimated for
prime-aged males derive in part from this problem.
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EMPLOYMENT CONTRACTS S45
the seller. The buyer thus profited to the extent that the price
charged per unit by the seller was less than the value indicated by
equation (1), and the buyer's demand curve for Q was thus the marginal
revenue curve derived from (1).
For the seller, profits were determined by a linear average cost
schedule,
AC = A + BQ, (2)
which gave the price per unit the seller was required to pay (to the
experimenter) to obtain as many units of the commodity as he sold to
the buyer. The seller thus profited to the extent that the price paid
per unit by the buyer was greater than the value indicated by (2), and
the seller's supply curve for Q was thus the marginal cost curve derived
from (2). After the negotiating pair reached agreement, they
were paid (by the experimenter) the actual level of profits implied by
their agreement.
The conception of these experiments was remarkably modern. In
their many bargaining games, the authors varied (a) bargainers' information
sets (complete vs. incomplete information regarding opponents'
objective functions), (b) the number of transactions per bargaining
pair (one-shot vs. repeated games), and (c) the price and
quantity at which profits were split equally between the two parties. In
addition, the authors went to great lengths to control for other factors
that might influence bargaining outcomes. For example, random assignment
was used whenever possible, and all bargaining was conducted
in total anonymity. Finally, the authors also varied the institutional
framework within which bargaining took place. In a first set of
experiments (Siegel and Fouraker 1960), bargainers were required to
make joint offers for a price and a quantity. A second set of experiments
(Fouraker, Siegel, and Harnett 1961), however, required the
seller to dictate a price to the buyer, who then chose a quantity to buy.
From the point of view of a bargaining pair taken jointly, it is
apparent that an efficient bargain should extract the maximum possible
rents from the experimenter and somehow allocate those rents to
the bargainers. In particular, the specific division of the returns between
the two parties should not influence the total profits obtained.
In this sense the pair of bargainers should act as a single individual.
Total revenues received by the bargainers from the experimenter
were Q - (AR - AC). It follows that, if the bargainers' utility levels
were linear in income, an efficient contract would select Q to max-
imize
joint profits = Q(AR - AC). (3)
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S46 JOURNAL OF POLITICAL ECONOMY
Simple differentiation, after the substitution of (1) and (2) into (3),
indicates that this requires the bargainers to exchange a quantity
QP = ~~~~~~~~~~(4)2(b + B)'(4
in which the superscript P denotes the Pareto-efficient outcome, determined
by the intersection of the bargainers' marginal revenue and
marginal cost curves. In a Pareto-efficient bargain, this quantity
should occur regardless of the price the bargainers agree on. The
price should determine only how the joint profits are split by the two
parties.
In most negotiations between workers and firms, we do not observe
joint decision making over the wage and employment level. This does
not necessarily imply that Pareto-inefficient trades are being made,
but it does at least suggest an alternative prediction for the employment
level that is not Pareto efficient. To proceed with the example,
suppose that the seller is given the right to unilaterally determine only
the price and that the buyer may then select the quantity purchased.
How will the seller determine the price to propose?
The classical solution due to Cournot and Bowley is to suppose that
the seller knows the buyer's demand curve. If the seller sets price P,
the seller may suppose that the buyer will maximize his own profits,
which are
1b = (AR -P) * Q. (5)
Taking P as fixed, as the buyer is assumed to do, substituting (1) into
(5), and differentiating shows that the buyer will respond by setting
marginal revenue equal to price, so that
a - 2bQ= P. (6)
The seller is then expected to maximize the seller's own profits subject
to the reaction function (6). This leads to the seller's maximizing
Hs = (P -AC) * Q, (7)
which, after substituting (2) and (6) and differentiating, leads to
QM = ~~~~~~~~~~(8)4b + 2B' 8
in which the superscript M denotes the monopoly outcome, a predicted
outcome different from QP.
In the Fouraker et al. (1961) experiments, the average revenue and
average cost curves (1) and (2) were known. It was thus possible to test
(4) and (8) as alternative predictors for the quantity transacted by
means of a simple comparison of predicted versus actual quantities
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EMPLOYMENT CONTRACTS S47
traded. In addition, because the simple monopoly model predicts that
observed price and quantity combinations will satisfy (6) and lie on the
buyer's marginal revenue schedule, whereas the model of Paretoefficient
transactions does not, a test of (4) and (8) could also be based
on the observed correlation of prices and quantities transacted.
Listed below in table 1, parts A and B, are summary statistics for the
bargaining outcomes presented in Siegel and Fouraker (1960) and
Fouraker et al. (1961). The first three columns of part A list, for the
case of simultaneous bargaining over prices and quantities, average
observed values (across bargaining pairs) for the ratio of transacted
quantities to the Pareto-optimal quantity (Q/QP); the ratio of transacted
quantities to the quantities that would be profit maximizing for
sellers as monopolistic price setters (Q/Q"'); and the ratio of transacted
quantities to those quantities that lie on buyers' demand curves at
actual transacted prices, Q!Qb(P). The remaining columns of part A
present results from regressions of transacted quantities on transacted
prices across bargaining pairs. With Pareto-efficient contracts,
these regression coefficients should all be zero, while in the simple
monopoly model, the absence of price variability would leave these
coefficients undefined. Failure by some sellers to charge the monopoly
profit-maximizing price might still leave (6) intact, in which case
the regression coefficient would be negative and equal to the slope of
the buyer's demand curve. Part B of the table presents information
similar to that in part A but for the case in which the seller dictates a
price to the buyer, who then chooses quantity unilaterally.
Beginning with part A, it is clear that, when bargaining takes place
jointly over price and quantity, the outcome very closely approximates
the Pareto-optimal solution. All observed values in column 1
are essentially unity and in no case differ statistically significantly
from unity. In contrast, no observed value in column 2 lies within
three standard errors of unity, indicating that transacted quantities
are not well predicted by the simple monopoly model. As column 3
shows, transacted quantities do not lie on the buyers' marginal revenue
curve. A simple regression of quantity on price yields a slope
estimate (fBq.t,) that is positive and far different from the known slop
of the buyer's marginal revenue curve for these experiments.
Consider now the summary statistics presented in part B. These
data describe the results of similar experiments conducted by
Fouraker et al. (1961) but in which sellers acted as price leaders,
unilaterally choosing a price, for which buyers then unilaterally chose
a corresponding quantity. As can be seen from column 1, transacted
quantities in this set of experiments no longer approximate the
Pareto-efficient value. It is also apparent that the information available
to the bargainers influences the outcome. In experiments 1 and
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S5o JOURNAL OF POLITICAL ECONOMY
2, the simple monopoly seller outcome is clearly a good description
of the data. The quantity transacted is about 30 percent reduced from
the efficient quantity but about equal to the prediction of the seller-asmonopoly
model. Likewise, the observed transaction price apparently
lies on the buyer's demand schedule. It is important to recognize that
experiment 1 involves multiple transactions, so considerable opportunity
is provided for the parties to build the long-term relationship that
might result in an efficient bargain. The bargainers apparently did
not establish such a relationship, perhaps because of incomplete information,
even though the results reported are for the final transactions
in the round.
The results of the third experiment, which involved complete information
and repeated bargaining, support neither the efficiency
prediction nor the simple monopoly prediction. Quantities transacted
are greater than what the simple monopoly model predicts but less
than the Pareto-efficient level. Nevertheless, the price and quantity
combinations observed fall along the buyer's demand curve, as indicated
by the results in columns 3 and 4 of part B. (The slope of the
buyer's marginal revenue curve is - 1 in this experiment.)
One might reasonably argue that little weight should be placed on
these experimental results, especially since the amount at stake in
these bargains was typically quite small. Moreover, these bargains
between two individuals may give only a poor indication of the relationship
that exists between many employees and a single employer.
As is always the case, it is necessary to find the parallels between the
laboratory setting and the observed institutions before firm conclusions
can be drawn. Nevertheless, we believe that these experiments
illustrate several important points.
First, the results indicate that differences in institutional settings
may have enormous effects on bargaining outcomes. This suggests
the importance of investigating models in which the determinants of
institutional types may be explained and of establishing empirically
when different institutional types are producing different outcomes.
Second, like all good experiments, the Siegel et al. results raise
questions that suggest the usefulness of further experiments. Two
areas for future investigation seem especially promising. In the repeated
transaction experiments, strikes (a failure to transact) were
observed. Casual observation suggests that these strikes may be a part
of the mechanism by which information is exchanged and bargains
are struck. Further experiments that explore the role of strikes in
bargaining may be useful since union-management bargaining appears
to result in similar behavior.3 Also, in the Siegel et al. experi-
3 See Coursey (1982) for a first step in such work.
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EMPLOYMENT CONTRACTS S51
ments, the institutional framework was determined by the experimenter.
It would be interesting to see how parties behave under the
same variety of information conditions but where they are also required
to agree on, or one party is allowed to select, the institutional
framework for subsequent bargaining. It would likewise be interesting
to explore the role that third parties, such as arbitrators or
insurance brokers, might play in these bargaining systems.
Finally, the Siegel et al. experiments provide an example of the type
of test one might apply to "field" data on wages and employment if
direct observations on firms' marginal revenue products and workers'
marginal utilities were available. With such data, determining whether
quantity transactions are efficient would be a relatively simple
matter, since tests could then be based on precise predictions for
quantities traded. In practice, however, the information on demand,
technology, and worker preferences required to implement such tests
with nonexperimental data is unlikely ever to be available. It follows
that "field" tests of the efficiency of employment determination must
be based on something else. To us, the best hope appears to lie in
observed correlations between wages and employment. As we have
seen, the Siegel et al. findings suggest that efficient contracts lead, if
anything, to negligible (or positive) correlations between price and
quantity across bargaining pairs, while inefficient contracts are associated
with a well-defined negative correlation between price and quantity
across bargaining pairs. In the following section we explore this
possibility more explicitly, with an eye toward subsequent empirical
application.
III. A Framework for Inference
As a prelude to our empirical work, we begin our analysis of employment
contracts with the traditional case in which unions are assumed
unable to provide insurance for unemployed workers and in which
third parties cannot serve this purpose either. We then consider the
alterations in our conclusions that are required when these assumptions
are relaxed.
A. Contracts without Worker Insurance
Consider a bargaining pair composed of an employer whose objective
is to maximize profits, defined as the difference between revenue
R(L) and the wage bill wL:
Tr(w, L) = R(L) - wL, (9)
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S52 JOURNAL OF POLITICAL ECONOMY
and a union, whose objective function is
u(w, L).4 (10)
Our starting point is the observation that a Pareto-efficient contract
must equate the marginal rates of substitution between wages and
employment for both the firm and the union. That is,
w - RL a u(*)IdL
L 'U( (1))lw
where R. denotes the marginal revenue produ
tive is to test whether observed data on wages and employment are
consistent with this condition.6
To develop our procedure, consider the following restatement of
condition (3):
RL = W(1 + Ew.L), (12)
where Ew-L = [(duldL)I(au/dw)](L
with respect to employment along the relevant iso-utility locus for the
union. As can be seen from condition (12), the efficient contract
chooses a level of employment such that the marginal revenue product
of labor is equated not with the contract wage but rather with a
measure of the marginal factor cost of labor, taking into account the
fact that the union will accept lower wages in exchange for higher
levels of employment. Because the union will generally place a positive
value on higher levels of employment, Ew.L will generally be negative,
implying that employment will generally exceed the level that the
firm would voluntarily choose at the contract wage.7
In what follows we assume that expressions (9) and (10) display strict concavity and
twice differentiability. With regard to the firm's profit function, these assumptions are
probably innocuous. With regard to the union "utility" function, however, these assumptions
seem less clearly justified. Establishing the mere presence of the function
u(w, L) in a bargaining unit with considerable heterogeneity in worker skills and wage
rates is akin to establishing the presence of a social welfare function for that unit. This
problem has been addressed by many writers. The famous dispute between Dunlop
(1944) and Ross (1948) may be interpreted as motivated by this and other issues.
Dunlop's view that it is useful to act as if union preferences may be represented as a
simple function u(w, L) is most plausible under those conditions in which all the workers
in the bargaining unit receive the same wage rate and face the same probability of
employment. Under these circumstances there is no social choice problem, and any
worker may be chosen at random to represent all other workers. We believe that the
printing and construction trades, from which many of Dunlop's examples are taken,
come closest to these conditions.
5 That is, we require that w and L be selected so as to maximize 7r(w, L) - X[u(w, L) u01]
for any U0, which leads to condition (11).
'3 For a similar treatment of this question, see MaCurdy and Pencavel (this issue).
7 The gap between the contract wage and employees' marginal value product is no
doubt related to what employers describe as "featherbedding." Strong trade unions
that can enforce featherbedding are often said to exist in the printing and construction
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EMPLOYMENT CONTRACTS S53
In contrast, consider now the case in which the union acts as a
monopolistic price setter, with the firm then choosing a most preferred
level of employment at the union's stated wage. In this case,
employment will be determined according to the condition that
R 1 = w. (13)
In comparison with condition (12), condition (13) provides an alternative
hypothesis that might allow a test for Pareto efficiency of employment
contracts. Conditions (12) and (13) suggest that one might study
the tendency for employment levels to equate marginal revenue
products either with (a) the contract wage or with (b) the marginal
factor cost of labor (where the latter is defined in condition [12]), in
much the same way that Fouraker et al. studied the tendency for
transacted quantities to approach either the Pareto-optimal value or
that value implied by a model of monopolistic price setting.8
Since we have no direct information about firms' profit functions
and unions' utility functions, however, we are unable to make any
direct comparison of actual and optimal employment levels. Instead,
we must focus our attention on the different implications of conditions
(12) and (13) for the correlations between employment levels,
contract wages, and alternative wages. In doing so, we are forced to
adopt some specific functional forms, and, not surprisingly, the manner
in which we interpret the data depends heavily on these assump-
tions.
To elaborate, suppose that the union utility function is such that
Ew,, is a constant. Suppose also that workers' marginal revenue pro
ucts are given by
log(RI.) = OtO + OtIX - 1X2 log(L), (14)
where X indicates other (unspecified) variables. In this case, conditions
(12) and (13) imply
log(L) = L ( - 0g(l + e-,.) + X - (i log(w), (15)
log(L) = (2+ ( 'X (-Ilog(w). (16)\ t2 / \ Q22
It is clear from conditions (15) and (16) that, as long as xt( is unknown
and Es,l.I is a constant, data on wages and employment cannot be used
to distinguish between the implications of conditions (12) and (13).
trades and in the railroad and entertainment industries. These industries therefore
seem like especially interesting candidates for testing efficiency in employment deter-
mination.
' This approach is also taken by MaCurdy and Pencavel (1984).
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S54 JOURNAL OF POLITICAL ECONOMY
Clearly, more structure must be imposed before any test based on
conditions such as (15) and (16) will be possible.
One method of providing such structure is to specify the union's
utility function in a way that Ew.L varies with observable variables tha
do not enter firms' profit functions directly. The most obvious candidate
variables for this role at an intuitive level are alternative wages
and employment opportunities for disemployed union members. If
we assume that these variables influence Ewl., equation (15) will then
include terms that are excluded from equation (16). In this case, a test
based on exclusion restrictions is possible.
If, for example, union preferences over wages and employment are
given by the Stone-Geary function
u(w, L) = k(w - w)3L 1 - , (17)
where - denotes some minimum acceptable contract wage, perhaps
equal to union members' alternative wage, condition (11) becomes
w -R (1 t )(w ) (18)
Equations (14) and (18) in turn imply an analogue to (15) given by
log(L) = -( +(a2 - (a ) log[yyw + (1 - -y)w], (19)
where y = (1 - P)/P. Notice that, unlike equation (16), eq
includes the alternative wage, w.
Equation (19) provides a useful framework within which to test the
hypotheses of strong efficiency and weak efficiency in employment
determination. To illustrate, consider the case where y is found to be
unity in the data. In this case, the alternative wage acts as the sole
determinant of employment (given X), with no influence from the
contract wage. Given such a finding, we would conclude that the data
are consistent with strong efficiency in employment determination.
Alternatively, if y were found to be less than unity but positive, both
the contract wage and the alternative wage would act as determinants
of employment. In this case, we would conclude that the data are
consistent with weak efficiency in employment determination. Finally,
if y were found to be zero in the data, the contract wage would act as a
sufficient statistic (given X) in determining employment, with no influence
from the alternative wage. In this case, we would conclude
that a model of monopolistic price setting by the union, with subsequent
unilateral employment determination by the employer, is the
most appropriate model for the data.
Because we can never know the exact forms of firm's production
functions and unions' utility functions, we can never be sure that the
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EMPLOYMENT CONTRACTS S55
data we study reflect the optimal correlation of wages and employment
implied by those particular functions. Nevertheless, except in
the extreme case in which unions place no value on employment, we
should find at least some negative employment effect of alternative
wages. Thus equation (19) provides one basic implication that might
be tested and on which normative conclusions might be based:
namely, that estimates of -y from (19) should be strictly positive. If we
maintain the assumption that unions place some positive value on
employment, we can argue that Pareto efficiency requires at least
weak efficiency in employment determination. Thus, if we fail to find
at least weak efficiency in employment determination, we can reject
the null hypothesis of Pareto-efficient employment determination.
At this stage we have a usable and yet still fairly general framework
within which to interpret the data. This framework focuses on the
employment effects of alternative wages (and other determinants of
unions' marginal rate of substitution between wages and employment)
in testing for Pareto efficiency in employment determination.
This framework has no testable implications, however, regarding the
employment effect of contract wages. It is worth asking, therefore,
what assumptions are required in order to base inferences on the
estimated effects of contract wages as well as alternative wages in tests
of Pareto efficiency in employment determination.
To develop such a framework, we take the union's objective function
to be the expected utility of the "typical" union member, given by
u(w, L) = (L-)g(w) + I (L )g (20)
where L denotes the number of union members actually employed by
the firm at a wage of w, L denotes the total number of union members,
L - L of whom are disemployed and must work elsewhere at a
wage of w, and g(-) denotes a twice-differentiable, concave function
relating worker's utility to realized earnings.9 When (20) is used in
place of the more general functions given by (10) or (17), condition
(12) becomes
RL = w + g(u) ,) g(w)1 .10 (21)
Taking a second-order Taylor series, expressions (14) and (21) imply
an employment equation given by
For simplicity, we assume that hours of work do not vary across jobs.
'0 This is the condition used throughout by McDonald and Solow (1981) in the
analysis of efficient employment contracts.
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S56 JOURNAL OF POLITICAL ECONOMY
log(L) - + ( )xI) log(( )
(22)
+ 2P [log(w) -log(U)]2,
where p denotes the Arrow-Pratt measure of relative risk aversion,
- wg"(w)/g' (w) .
In comparison with equation (19), equation (22) provides a somewhat
less general but potentially more powerful framework within
which to test the null hypothesis of Pareto-efficient employment determination.
Like equation (19), equation (23) implies a negative employment
effect for alternative wages. Unlike equation (19), however,
equation (22) also provides implications regarding the Paretoefficient
employment effect of contract wages. In particular, it can be
seen that equation (22) involves no first-order term in log(w). Within
this framework, the contract wage influences employment only
through higher-order terms in the logarithmic difference between w
and -w. Thus, within this framework, one might base a test of Paretoefficient
employment determination on the absence of any first-order
employment effect of the contract wage, in addition to the previously
required negative employment effect of the alternative wage.
Further restrictions on the form of the union utility function suggest
an even more powerful test. In the special case where g(w) is
linear, so that p is equal to zero, equation (22) reduces to
log(L)= (?2) + (2 )X- (i)log(uw), (23)
which is just the strong efficiency hypothesis. Thus, if we maintain the
assumption that workers are risk neutral, we can then argue that
Pareto efficiency requires what we have called strong efficiency in
employment determination. Granted, it is unlikely that workers are
risk neutral, and so it may seem that rejection of Pareto efficiency on
the basis of (23) is not very significant. In the next section, however,
we provide an argument that suggests a more general justification
and interpretation of this test.
B. Contracts with Uncertainty and Insurance
Much of the literature on "implicit contracts" explores the extent to
which uncertainty and imperfect information alter the form of
efficient contracts in circumstances of bilateral monopoly. One important
prediction from such models is the increased likelihood that employment
contracts will be strongly efficient. It is instructive to see why
this is the case because it shows how providing greater institutional
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EMPLOYMENT CONTRACTS S57
flexibility can change the predictions of the simplest bilateral monopoly
models.'
To be precise, suppose again that the union's objective function
takes the expected utility form in (20). Suppose further that we allow
the union to tax employed workers an amount zD in order to make
payments of ib to disemployed workers. Financing this unemployment
insurance scheme requires that zvL = zb(L - L), and maximization
of (20) with respect to zi and zw subject to this constraint leads to
the first-order conditions
g, ( + 7w) - g (U) + ZW) = x(L - L), (i
_ (w - zv) = L. (ii)
Eliminating A by taking the ratio of these two equations establishes
that g(w + zw) = g(w - zv), which implies that union members are
fully insured. Moreover, since w + zi = w - zv, it follows that each
worker's utility is g(w + zi) = g{(LIL)w + [1 - (LIL)]-W}, which by
condition (21) implies that RI, = , the strong efficiency hypothesis. Thus
there is some basis, beyond arbitrary functional form restrictions, for
expecting employment contracts to display strong efficiency.
The presence of worker risk aversion in a model of bilateral monopoly
should lead to worker demands for income insurance. If this
insurance is complete, workers will be indifferent to the risk of disemployment,
and observed wage-employment combinations will be consistent
with the strong efficiency hypothesis. Therefore, if one maintains
a utility function for workers of the form (20), it follows that
rejection of the strong efficiency hypothesis in the presence of Pareto
efficiency requires more than just the absence of risk neutrality. Such
a rejection requires also that there exist some human or technical
obstacle to the contractual provision of income insurance.
Finally, it is worth considering how these conclusions may be
modified if workers are unable to observe R., the value of their work
to the firm. It is tempting to conjecture that this might lead the parties
to a contract that contains some elements of both the efficient contract
and monopoly price-setting models, but as far as we are aware, this
has not been established in any formal model. This may serve as a
reminder that there is still considerable research necessary before the
relationship between the various models and their empirical implications
is fully established. Perhaps this also implies that our empirical
approach should at this stage proceed without forcing unnecessary
structure onto our data analysis.
l We are indebted to Oliver Hart for suggesting the following argument.
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S58 JOURNAL OF POLITICAL ECONOMY
IV. Empirical Implementation
Our empirical work makes use of data on membership and contract
wages for 10 locals belonging to the International Typographical
Union (ITU) for the period 1948-65.12 The choice of this union was
motivated by several practical considerations. First, the union itself
publishes data on membership and wages for each of its member
locals, and related data on output, product prices, and factor prices
for the newspapers employing ITU members are also readily available.
Second, the ITU is remarkably democratic in its operation and
decision making, while the nature of members' jobs is fairly homogeneous
across locals. In addition, although the ITU sets some bargaining
guidelines at the national level, individual locals bargain independently
with regard to wages, hours, and corresponding levels of local
employment. As a result, the ITU data appear to provide an opportunity
for measuring the employment effects of contract wages and
alternative wages in a setting in which unobservable job-specific and
person-specific characteristics do not vary much across locals but in
which wages and employment do vary across locals. Third, newspaper
industry disputes over employment levels are both commonplace and
long-standing. This suggests that the newspaper industry may be a
good candidate for testing the efficiency of employment determination
since the presence of joint bargaining over wages and employment
may indicate some separation between the distributional and
allocative effects of contracted wages.
As is typically the case with empirical work, however, our data fail
to perfectly match the theoretical constructs we have emphasized in
equations such as (19) and (22). We have thus been required to maintain
a number of assumptions in our interpretation of the data. The
most important of these assumptions concern the measurement of
employment, alternative wages, and demand-related variables in our
analysis. These assumptions are discussed in detail in Appendix B.
On the basis of the many considerations listed in Appendix B, we
have used several alternative specifications in our tests for employment
efficiency. With regard to employment, we have used four alternative
measures. These are (i) the number of journeyman printers
who are members of a union local; (ii) the number of "active" members
of a union local, defined as the number of journeyman members
plus the number of apprentices minus the number of retired journey-
12 The time period 1948-65 was chosen to avoid complications arising from techno
logical innovations that occurred in the printing industry after 1965. Summary statistics
and definitions of variables are presented in App. A. We are indebted to John Pencavel
for providing us with a substantial portion of these data. For previous analyses based on
these data, see Dertouzos and Pencavel (1981) and Pencavel (1984).
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EMPLOYMENT CONTRACTS S59
man members; (iii) an imputed measure of total local hours, h,
defined as the ratio of local assessments to the product of the local
wage and the aggregate ITU assessment rate; and (iv) local assess-
ments.
With regard to alternative wages, we have used 11 different measures
of the alternative wage relevant to ITU printers. These are (i)
the real average hourly earnings of production workers in all U.S.
manufacturing industries; (ii) the real average hourly earnings of
production workers in all manufacturing industries in the local's census
region; (iii) the real average hourly earnings of production workers
in all manufacturing industries in the local's state; (iv) the real
average hourly earnings of production workers in all U.S. printing
and publishing industries; (v) the real average hourly earnings of
production workers in all printing and publishing industries in the
local's census region; (vi) the real average hourly earnings of production
workers in all printing and publishing industries in the local's
state; (vii) the real average weekly contract wage for ITU journeyman
printers in all U.S. locals; (viii) the real average weekly contract wage
for ITU journeyman printers in the local's state; (ix) the real average
hourly contract wage for ITU journeyman printers in an "adjacent"
local; 13 (x) the real average hourly earnings of nonsupervisory workers
in all U.S. retail trade establishments; and (xi) the real average
hourly earnings of production workers in all U.S. durable goods
manufacturing industries.
A. Instrumental Variables Estimates
For each measure of employment and for each measure of the alternative
wage, we first estimated the Stone-Geary specification (19) and
the expected utility of employment specification (22). In these
specifications, the vector X included local-specific fixed effects, localspecific
linear time trends, a common quadratic time trend, the
logarithm of the average real advertising rate for the newspapers)
employing local printers, the logarithm of the total advertising linage
for the newspapers) employing local printers, and, as discussed in
Appendix B, the lagged value of the dependent variable.' Finally,
13 For this purpose, locals were matched according to geographical proximity. The
exact pairings are given in App. A.
"' In addition, we also included a dummy variable to account for newspaper mergers
and dummy variables for two observations that we think reflect strike activity (Memphis,
Tenn., 1952, and Augusta, Ga., 1965). Also, for the equations using assessments
as the dependent variable, current and lagged values of the contract wage and of the
aggregate ITU assessment rate were initially included in the vector X, along with
lagged values of assessments. It was readily apparent, however, that these three lagged
variables were duplicating the effect of lagged imputed hours since the estimated
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S6o JOURNAL OF POLITICAL ECONOMY
following our discussion in Appendix B, we have used current and
lagged values of the consumer price index and lagged values of the
contract wage as instruments for the current contract wage.
Our results from estimating equations (19) and (22) were uniformly
poor. In the case of (19), the parameter My was repeatedly found to be
negative and large, while, in the case of (22), the estimated coefficient
for the squared term in [log(w) - log(W)] was typically much larger
than one in absolute value and frequently of the wrong sign to support
the hypothesis of risk aversion. In addition, the standard errors
for these estimates were quite large.
At this stage, it was apparent to us that the framework provided by
equations (19) and (22) would not allow us to study the data in an
informative way. We therefore chose to focus instead on a first-order
approximation to (19) and (22) given by
log(L) () + -X) (I) log(u)) - ( O )log(w). (24)
Equation (24) can also be interpreted as a general nesting equation
for the two models given by (16) and (23), where the parameter 'y
measures the relative weight the data give to each model.
Listed in table 2, parts A-D, are the results of fitting equation (24)
to our pooled data from 10 ITU locals. Part A presents estimated
equations for which the dependent variable is the (log) total number
of journeyman printers. Eleven equations are presented, one for each
measure of the alternative wage. Parts B-D present similar equations
for which the dependent variables are (log) "active" membership,
imputed hours, and assessments, respectively.'5
Beginning with part A, we find no consistent evidence that alternative
wages negatively influence employment (as measured by journeyman
membership). With the one (marginal) exception of row 9, the
coefficients for lagged wages and assessment rates were approximately equal and both
approximately equal to the negative of the estimated coefficient for lagged assessments.
Given this fact, to improve the precision of the instrumental estimates, we substituted
lagged imputed hours in place of lagged assessments, wages, and assessment rates in
the assessment equations.
15 The columns headed p in these tables present estimated coefficients from supplementary
equations based on the residuals taken from our employment equations.
For each employment equation we retrieved the residuals (e,) and then estimated the
equation
et = 8() + 8,IX, + 82 log(w,) + 83 log(w,) + 854 log(L, -) + pEt l + v. (*)
We use our estimates of p from this supplementary equation as a basis for a test of firstorder
autocorrelation in our error terms. A more straightforward approach would be
to use the Dubin h-statistic, but for our data the h-statistic is typically not defined since
its computation requires us to take the square root of a negative number. Finally, we
should mention that there is no evidence of any serial correlation among the v, from eq.
(*)
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EMPLOYMENT CONTRACTS S6 1
estimated coefficient for the alternative wage is never statistically
significantly negative. We also find, however, no clear evidence that
contract wages influence employment. Indeed, in every equation presented
in part A, the estimated effect of contract wages on employment
is positive rather than negative. Although this finding is consistent
with efficient employment determination (with Stone-Geary
utility, e.g., y will exceed unity and employment will be positively
related to contract wages whenever 13 is less than .5) and is reminiscent
of the findings of Siegel and Fouraker (1960), we suspect this finding
derives as much from sampling error as from anything else. Apparently,
the instruments we have at our disposal will not allow us the
precision with which any clear conclusions might be drawn from these
data.
On the basis of the alternative measure of employment that excludes
retired journeymen but includes apprentices, there is perhaps
a bit more evidence of efficiency in part B than in part A. The difference
is very small, however. The estimated coefficients for alternative
wages are more uniformly negative in part B than in part A, while the
estimated coefficients for contract wages remain predominantly positive.
Unfortunately, however, as was true for part A, the coefficient
estimates in part B are too imprecise to allow any substantive con-
clusions.
Consider now the estimates presented in part C, which are based on
earnings-related data rather than membership counts (as discussed in
App. B, we take local-specific assessments to be a measure of localspecific
earnings). In contrast to the estimates presented in parts A
and B, these estimates are more consistent with monopolistic wage
setting by the union and unilateral employment determination by the
firm than with joint employment determination. It is now the alternative
wage that frequently has a positive estimated coefficient, while the
contract wage effect is consistently negative although generally statistically
insignificant.
Part D of table 2 presents results very similar to those in part C. In
this case, since the dependent variable is the logarithm of assessments,
the effect of contract wages on employment is measured by the difference
between the estimated contract wage coefficient and unity. As
was true for part C, the implied contract wage effect in part D is
typically negative but not significantly different from zero. The estimated
employment effect of alternative wages is never significantly
negative and frequently of the wrong sign, as was true in part C.
Given the inconclusive results presented in table 2, we have reconsidered
our measurement of alternative wages. In particular, we have
relaxed our implicit assumption that disemployed union members
can find certain and instantaneous employment at the alternative
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S66 JOURNAL OF POLITICAL ECONOMY
wage. This was done by including as a regressor in our previous
equations the logarithm of one minus the relevant state-insured unemployment
rate. In the context of a monopoly model of union-firm
interaction, this variable should, like alternative wages, have no influence
on employment except insofar as it influences the contract
wage. Thus, if the monopoly union model is appropriate, this unemployment
variable should have an estimated coefficient of zero. Alternatively,
if an efficient contracting model of employment determination
is appropriate, this variable, like alternative wages, should have a
negative effect on local employment of ITU printers.'6
The results of estimating these augmented equations are presented
in table 3, parts A-D. As can be seen from this table, the basic
findings of table 2 remain. In particular, on the basis of membership
data (table 2, pts. A-B), alternative wages typically have a negative
but statistically insignificant effect on employment, while contract
wages typically have a positive (also insignificant) effect on employment.
On the basis of earnings-related data, however, these findings
are reversed. In table 3, parts C and D, the estimated coefficients
for alternative wages are frequently positive, while estimated contract
wage effects are always negative (but generally statistically
insignificant).
In contrast to the absence of any systematic wage effects in these
data, consider now the estimated coefficients for alternative employment
probabilities. These estimated coefficients are negative in every
row of table 3. They are relatively small (and statistically insignificant)
in parts A and B, but they are much larger (and frequently statistically
significant) in parts C and D. These estimated coefficients are consistent
with efficiency in employment determination, for they indicate
that, as alternative employment opportunities (and wages expected
over states of unemployment and employment) improve, employment
at ITU locals is reduced. Only if the demand for printers' services
were countercyclical would these estimated effects of alternative
employment probabilities be consistent with a monopolistic model of
union-firm interaction. Thus, in table 3, parts C and D, the data
provide at least some limited evidence of (weak) efficiency in employment
determination.
16 This statement abstracts, of course, from any other sources of correlation between
statewide unemployment rates and the error term in our employment equations. It is
worth noting that if alternative employment status were a binomial variable with probability
1 - U and if workers were risk neutral, the appropriate alternative wage measure
to include in our regressions would be the (logarithm of the) product w(1 - U). A
simple test of this specification could then be based on the difference between the
separate coefficients estimated for log(w) and log( 1 - U). As will be seen, the estimated
coefficients for log(w) and log(l - U) are nowhere near equal.
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EMPLOYMENT CONTRACTS S67
At this point it is useful to investigate more closely the characteristics
of our data that have generated the instrumental estimates presented
in tables 2 and 3. As it turns out, there are a few simple facts in
the data that appear to be responsible for our findings. In particular,
on inspection of the reduced-form equations underlying tables 2 and
3, we repeatedly find that the three variables used as instruments for
the contract wage (current and lagged consumer prices and the,
lagged contract wage) all have large and statistically significant reduced-form
effects on wages but have no statistically significant reduced-form
effects on employment. Thus another (and perhaps
more straightforward) way to describe the findings of tables 2 and 3 is
to say that lagged wages and prices have large positive effects on
current (real) wages and that current prices have large negative effects
on current (real) wages, but that none of these variables has any
statistically discernible effect on current employment. Given this fact
and given that these three variables are the only instruments we use, it
is not surprising that our estimated structural equations show no statistically
discernible employment effect of contract wages.
What can we infer from tables 2 and 3? Because membership-based
data cannot capture variation in hours per employed member or
employed members per total membership, we are inclined to place
greater weight on estimates derived from earnings-related data. We
are encouraged, moreover, that the estimated contract wage effects
based on imputed hours (discussed in App. B) are so similar to those
based directly on assessments. These considerations, along with the
apparent statistical importance of alternative employment probabilities,
lead us to emphasize the results presented in table 3, parts C and
D. On the basis of these parts of table 3, we find some support for at
least weak efficiency in employment determination. The data suggest
that contracts do take workers' alternatives into account in determining
employment. The data are less informative, however, as to the
employment effects of contract wages and alternative wages.
B. Ordinary Least Squares Estimates
The conclusions that we draw from tables 2 and 3 derive in large part
from the fact that lagged prices and wages influence current wages
but do not influence current employment. It is a large step to go from
this finding to a statement about the efficiency of employment contracts,
and we cannot be certain that this step is justified. It may be
instructive, therefore, to compare our instrumental variables estimates
with ordinary least squares (OLS) estimates of the same equa-
tions.
Presented in table 4, parts A-D, are OLS estimates analogous to the
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S76 JOURNAL OF POLITICAL ECONOMY
instrumental variable (IV) estimates presented in table 3.17 In comparison
with these IV estimates, two basic findings are apparent. First,
for membership-based measures of employment, the OLS point estimates
are not substantially different from the previous IV point estimates.
There is a clear tendency for the OLS coefficients on both the
contract wage and the alternative wage to be smaller in absolute value
than the corresponding IV estimates (see, e.g., rows 1, 7, and 11 of
table 4, pts. A-B), but the basic nature of the results is unchanged.
There is little evidence of any wage effects on employment in parts A
and B and only marginal evidence that alternative employment probabilities
have any influence on employment. Perhaps the wage bargains
struck by the locals in our sample are not greatly influenced by
membership levels. If so, this might explain the congruence between
table 3, parts A-B, and table 4, parts A-B. An alternative explanation,
of course, is that these membership-based measures of employment
are so poor that, regardless of our estimation method, no clear
relationship can be uncovered.
The second finding in table 4 is that, for earnings-based measures
of employment, there is a substantial difference between OLS and IV
estimated wage effects. In particular, the OLS estimates of the employment
effects of contract wages tend to be much larger in absolute
value in table 4, parts C-D, than the corresponding IV estimates in
table 3, parts C-D. In addition, the standard errors for the estimated
contract wage coefficients are substantially reduced. The consequence
of these two facts is that, for every measure of the alternative wage in
table 4, parts C and D, the contract wage maintains a statistically
significant negative effect on employment. In contrast, the estimated
alternative wage effect is consistently positive and frequently statistically
significant. At the same time, it remains true that greater alternative
employment probabilities reduce local employment. Indeed, both
the coefficient estimates and standard errors for the employment
probability variable are changed only slightly in going from IV to
OLS.
One obvious explanation for the pronounced contract wage effects
in table 4, part C, is that the dependent variable is based on a ratio, the
denominator of which is the contract wage. If the contract wage is
measured with any error, this measurement error will bias the estimated
contract wage coefficients toward negative one. The estimated
contract wage effects in part C certainly suggest that this
problem is present.
Consider, however, the estimated contract wage coefficients in part
17 For the sake of brevity, we discuss only those equations including the employment
probability variable, log( 1 - U).
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EMPLOYMENT CONTRACTS S77
D. There is no mechanical or definitional tendency for these
coefficients to be biased, and yet they imply virtually the same contract
wage effects as indicated by part C. In particular, the estimated
wage coefficients in part D are typically several standard errors below
unity. Put simply, increases in contract wages are not associated with
anything near equal proportionate increases in assessments, with the
ITU assessment rate held constant. Our reading of this fact is that
hours per employed member or employed members per total membership
must be falling as the contract wage increases. We are inclined,
therefore, to interpret part D as providing additional evidence
that employment contracts are not strongly efficient. At the very least,
we find no overwhelming evidence consistent with strong efficiency.
We do continue to find evidence consistent with weak efficiency,
however. As was true in table 3, parts C-D, higher alternative employment
probabilities reduce local employment by a statistically
significant amount. This fact could be explained by a negative correlation
between general levels of demand and unmeasured elements of
the demand for printers' services, but such a negative correlation
seems quite unlikely to us.18 Our interpretation of the ITU data,
therefore, is that strong efficiency does not seem to be present, but
weak efficiency cannot be rejected. We therefore cannot reject the
null hypothesis of Pareto efficiency in employment determination.
V. Concluding Remarks
A meaningful distinction between efficient and inefficient employment
contracts under bilateral monopoly exists only when employees
(or their unions) value the overall level of employment in their firm.
When a meaningful distinction exists between efficient and inefficient
employment contracts, public policies that weaken trade unions will
have different effects on employment according to whether employment
contracts are struck as efficient bargains. Likewise, the welfare
cost of trade union "wage distortions" is a meaningful concept only
when employment bargains are inefficient since the absence of the
welfare cost of union wage distortions is precisely what characterizes
an efficient employment bargain. It follows that the empirical determination
of whether employment bargains are struck efficiently is of
considerable practical importance.
18 For the 10 locals contained in our data set, the correlation between log(lin
log(l - U), corrected for trends and fixed effects, is .316, with a probability value of
.0001. For the ITU as a whole, the corresponding correlation is .464, with a probability
value of .052. Given the clear positive correlation between printers' output and alternative
employment probabilities, it seems unlikely to us that a negative correlation exists
between unmeasured elements of demand and alternative employment probabilities.
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S78 JOURNAL OF POLITICAL ECONOMY
Much of the recent literature on employment contracts emphasizes
that it is in the interests of the parties to produce institutional arrangements
that lead to employment contracts that we have termed
"strongly efficient." Strong efficiency implies that employment is set
so as to equate the marginal revenue product of workers to their
alternative wage. It follows that employment in such contracts fluctuates
with the determinants of a worker's marginal revenue product
and with the worker's alternative wage, but not with the observed
contract wage.
We have examined two kinds of evidence to test the strong
efficiency hypothesis. Laboratory experiments by Siegel et al. indicate
that this hypothesis is strongly confirmed when the bargaining parties
are required to agree on price and quantity simultaneously and is
strongly rejected when the parties are required to bargain by a system
of price leadership. In our field data on the printing trades, we find
no convincing evidence of strong efficiency. This is also MaCurdy and
Pencavel's (this issue) finding. When we use membership-based measures
of employment, we typically find no statistically significant employment
effect of contract wages. We also find, however, no statistically
significant employment effect of alternative wages or alternative
employment probabilities. Thus we are hesitant to make too much of
the fact that contract wages have no statistically discernible effect on
membership-based measures of employment. When we make use of
earnings-related measures of employment, we find some evidence
that contract wages do influence employment negatively. When instrumental
variables techniques are used, the estimated employment
effect of contract wages is always negative although imprecisely measured.
When ordinary least squares is used, the estimated employment
effect of contract wages is uniformly negative and always statistically
significant.
We have also examined the evidence in support of what we have
called the "weak efficiency hypothesis." According to this hypothesis,
both the contract wage and the alternative wage determine employment.
To examine this hypothesis, we have searched for convincing
evidence that some measure of the alternative wage is a determinant
of employment in our field data on the printing trades. We have
found some support for this hypothesis in the negative effects of
alternative employment probabilities on local employment of ITU
printers. However, we have also found that our measures of the alternative
wage available to workers are frequently positively related to
employment, precisely the contrary of the hypothesized direction of
this effect in a weakly efficient contract.'9
19 MaCurdy and Pencavel (this issue) report negative effects for the alternative wa
in their study of employment in the printing trades, but it is difficult to judge the
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EMPLOYMENT CONTRACTS S79
It seems clear that further research will be required before any of
the simple contracting models of employment determination that we
have examined here are likely to be useful positive tools in the analysis
of public policies toward the labor market.
Appendix A
Definitions and Sources for Variables Used
in the Empirical Analysis
Measures of Employment, Earnings, and Contract Wages
Data for the following variables were taken from annual statistical supplements
to the TypographicalJournal and from various issues of the ITUJournal.
w = local hourly contract minimum-wage scale (as of May 20);
M = local "active" membership, defined as total journeyman members plus
apprentices minus journeyman members on pension (as of May 20);
J = local journeyman membership (as of May 20);
A = local assessments during the fiscal year ending May 20;
0 = ratio of the total ITU assessments during the fiscal year ending May 20
to total ITU earnings during the fiscal year ending May 20.
Measures of Demand for Printers' Services (X)
Data for the following variables were taken from April issues of Editor and
Publisher and from annual issues of Editor and Publisher's International Year
Book: (i) average real advertising rate per line charged by the newspapers)
employing local printers (measured by calendar year); (ii) average yearly
advertising linage for the newspapers) employing local printers (measured
by calendar year).
Measures of Alternative Wages (W)
Data for the following measures were taken from Employment and Earnings,
United States, 1909-75, and from Employment and Earnings, States and Areas,
1939-78: (i) national average for hourly earnings of production workers in
all manufacturing industries; (ii) national average for hourly earnings of
nonsupervisory workers in retail trade; (iii) national average for hourly earnings
of production workers in all nondurable goods manufacturing industries;
(iv) national average for hourly earnings of production workers in SIC
27 (printing and publishing); (v) state average for hourly earnings of production
workers in all manufacturing industries; and (vi) state average for hourly
earnings of production workers in SIC 27 (printing and publishing).
Data for the following measures were taken from annual issues of the
Annual Survey of Manufactures and of the Census of Manufactures: (vii) regional
statistical significance of this result. It is our impression that the relevant coefficient is
statistically significant in a linear specification of the right-hand side of our eq. ( 11) and
is not statistically significant in a specification based on the Stone-Geary utility function,
(17) above. However, .MaCurdy and Pencavel do not require statistically significant
evidence that the alternative wage influences employment to conclude that the data
favor the weak efficiency hypothesis.
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EMPLOYMENT CONTRACTS S81
average for hourly earnings of production workers in all manufacturing industries
(this variable was calculated as the ratio of total wage payments to
production workers divided by total hours of production workers for the
relevant census region); and (viii) regional average for hourly earnings of
production workers in SIC 27 (printing and publishing) (this variable was
calculated as the ratio of total wage payments to production workers divided
by total hours of production workers for the relevant census region).
Data for the following measures were taken from annual statistical supplements
to the Typographical Journal: (ix) national average for ITU contract
minimum weekly wage scales; (x) state average for ITU contract minimum
weekly wage scales; and (xi) hourly ITU contract minimum-wage scale for an
"adjacent" local. Pairings were as follows: (Cincinnati, Columbus); (Dubuque,
Fond du Lac); (Memphis, Louisville); (Augusta, Columbia); (Elmira, Albany).
All nominal values were deflated by the consumer price index (all items).
For the equations in which log(l - U) was included as a regressor, the
variable U was measured as the state-insured unemployment rate, taken from
the March 1964 and March 1966 issues of the Manpower Report of the President.
Data for the following locals were used in our empirical analysis: Cincinnati,
Ohio; Augusta, Georgia; Columbia, South Carolina; Dubuque, Iowa;
Memphis, Tennessee; Fond du Lac, Wisconsin; Louisville, Kentucky; Elmira,
New York; Columbus, Ohio; Albany, New York.
We are indebted to John Pencavel for providing us with some of the data
on which our work is based. For earlier work based on data for these locals,
see Pencavel (1984) and Dertouzos and Pencavel (1981).
Descriptive statistics for the variables used in our analysis are presented in
Table Al.
Appendix B
Problems of Empirical Implementation
Measuring Employment
A major shortcoming of our data is that they provide no direct measure of
local employment. Instead, we are provided only with measures of local
membership. 20 If we are to interpret our membership data as employmen
we must first assume that the disemployed members of each local, denoted by
(L - L) in the context of equation (20), have already left the local, so that
observed membership reflects L and not L. Clearly, such an assumption is
problematic, especially since the differences between local membership and
local employment may not be independent of the contract wage.
In an attempt to deal with this problem we have also made use of data on
local dues paid to the national union to construct an alternative, imputed
measure of actual employment at the local level. By definition,
Ait = Oitwfthit, (B 1)
20 Local membership data are further broken down
and apprentices. The ITU also reports for each local the number of members on
pension. Consequently, it is possible to measure the number of "active" journeymen by
taking the difference between total journeyman members and members on pension.
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S82 JOURNAL OF POLITICAL ECONOMY
where Ad denotes assessments (d
assessment rate for local i in year
year t, and hi denotes total man-hours worked for local i in year t.21 We have
no direct measures for 0it or hit, but we can observe O, the overall assessment
rate for the ITU as a whole, and Mi, "active" membership for local i in year t.
Therefore, if we assume that 0it can be written as X-Ot and that hit can be
written as TiM tV-t, where Xi and Tv are local-specific constants and vit reflects the
intertemporal variation of hours per active member in local i, equation (B 1)
can be rewritten as
A-t = XivTOtW-tM-tV-t (B2)
Taking logarithms, we can restate equation (B2) as
log(A-t) = log(Xsr-) + log(Ot) + log(wit) + log(Mit) + log(vit). (B
Treating (B3) as a regression equation, with log(vzt) as the unobserved error
term, we found the following estimates for the 10 locals comprising our data
set:22
log(A t) = local-specific intercepts + .982 log(6t) + 1.011 log(w-t)
(.021) (.065)
+ .951 log(Mit) + eit,
(.070)
R2 = .997, D-W = 1.860, df = 176.
These estimated coefficients seem sufficiently close to those implied by (B3) to
warrant treating the logarithm of (Ajt/0t)w1t as a measure (up to a constant
term) of the logarithm of total man-hours for local i in year t. Consequently,
we have used as a dependent variable in our empirical analysis the imputed
measure kit, defined as
hit = log(A-t) - log(Ot) - log(w-t). (B4)
Finally, as an alternative and less restrictive procedure, we have also used
local-specific assessments as the dependent variable in equations such as (19)
and (22), with wit, Ot, and local-specific dummies included as regressors. In thi
case, the absence of any contract wage effect on employment would translate
into a coefficient of unity for the contract wage, while a negative employment
effect of alternative wages would translate into an equivalent negative effect
on (log) assessments.
Measuring Alternative Wages
We also face problems with regard to the measurement of alternative wages.
On the one hand, we run the risk of choosing an irrelevant measure for the
alternative wage, in which case the data would seem to reflect an absence of
21 Assessment rates may vary over time and across locals because of differences in the
proportions of apprentices, journeymen, and pensioned and unemployed members
across locals.
22 We are indebted to David Card for several useful discussions regarding this approach.
Equation (B2) was also estimated in a manner that allowed the coefficient for
log(01) to vary across locals. The resulting estimates were essentially identical to those
reported here.
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EMPLOYMENT CONTRACTS S83
even weak efficiency in employment determination, with the contract wage
reflecting both its own effect on employment and some portion of the employment
effect of the unobserved alternative wage. On the other hand, even
if we have chosen the correct measure for the alternative wage, this alternative
wage may be so highly correlated with the contract wage that estimation
of the two variables' separate effects may be impossible. Realizing the potential
for these problems, but having no clear basis for choice of an alternative
wage measure, we have chosen to use several alternative measures that we
believe may be relevant. Each measure corresponds to a different assumption
regarding the distribution of alternative wage offers confronting disemployed
printers, and while we have no way of knowing which, if any, of these
assumptions is valid, it seems likely that at least one of them may provide
some useful information.
Measuring Demand-related Variables
ITU printers may typically be employed either by newspapers or "job" establishments.
In our empirical work we require data that reflect firms' demands
for printers' services (e.g., output, product price, and advertising rates). Such
data are reasonably available only for newspapers, however, and so we have
no measures of demand-related variables directly relevant to those printers
employed in job establishments. Moreover, the data do not allow us to identify
which members of a local are employed by news (or job) establishments.
Therefore, to whatever extent the printers in our sample are employed by job
establishments and to whatever extent the determinants ofjob establishments'
demand for printers' services differ from those of news establishments, our
empirical work will be subject to error.
Now that the most obvious limitations of our data have been discussed, it
remains for us to discuss four additional sources of potential problems in our
interpretation of the data, all of which fall under the general heading of
misspecification. The first of these concerns our ability to control for other
factors that might enter firms' production functions. The second concerns the
presence of additional constraints on firms' behavior and, in particular, the
possibility that a fixed-output framework might be more appropriate for our
analysis. The third concerns the question whether our interpretation of the
data would remain valid when placed in an explicitly dynamic framework.
Finally, the fourth source of potential problems concerns the issue of
identification.
Controlling for Other Factors Entering Firms' Production Functions
To this point we have implicitly assumed that firms are price takers in the
market for all other factors of production and that the effects of variations in
the rental prices of these other factors can be taken into account in our
statistical work. Obviously, this is a difficult task made even more difficult by
the fact that we have no direct measures for local employment of other factors
of production and only very limited measures of rental prices for other factors
of production. The only factor price data we have are annual observations
on (1) the price of newsprint and (2) the BLS wholesale price index for
machinery and equipment. Both of these price indexes are aggregate measures
that are common across locals. Thus we have no real ability to allow for
cross-local variation in the employment or rental prices of other factors and
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S84 JOURNAL OF POLITICAL ECONOMY
only limited ability to control directly for intertemporal variation in these
variables. Because of these data limitations we have assumed that firms' production
functions are of the constant elasticity of substitution form so that
printers' (log) marginal products can be expressed in terms of employment
and output alone. To the extent this assumption is invalid, our inferences will
be subject to error.
Allowing for the Possibility of Quantity Constraints
In Section III of the text we treated output as endogenous to the firm. There
may, however, be some cases in which it is more appropriate to treat output as
exogenous for the firm. This would surely be the case, for example, if one
were studying a regulated industry that was constrained to offer some
minimum level of service. Alternatively, in an industry such as newspaper
production, which is characterized by continuously increasing returns to
scale, output may not be determined by the usual marginal conditions.23 It
may therefore be worthwhile to describe briefly how our analysis would be
changed in the case of exogenous output constraints.
To deal with the fixed-output case, consider the "other inputs" requirement
function, K = K(L, Q), which gives the other inputs necessary to produce
Q units of output when L units of labor input are used.
Given that Q units of output are to be produced, the usual minimization of
costs subject to a utility constraint leads to an efficiency condition analogous to
( 1) of the form:
w - rKL _= au(-)l (B5)
L au(-)law
where r denotes the rental rate for capital.
The empirical analysis can now proceed exactly as before, with the function
rKL,(L, Q) replacing the marginal revenue function RI, (L, K) throughout. Th
main difference between this case and the case in which output is chosen
freely by the firm is that in this case the rental prices for other factors of
production should enter into any estimated employment equation. In addition,
any empirical specification must obviously allow for interactions between
rental prices and the marginal rate of substitution function KL. The advantage
of this model is that it is consistent with a situation in which union and
management bargain over capital/labor or man/machine ratios but output is
not determined in this way.
Amendments Suggested by a Dynamic Framework
Our discussion in Section III made no distinction between short-run and
long-run employment determination. Our implicit assumption has been that
the data reflect a sequence of equilibria generated from a static model. This
assumption should be questioned, especially since there is so much other
evidence of serial correlation in employment equations and since the whole
context of our discussion is one in which there is some fixity in employment
relations. It is beyond the scope of this paper to deal exhaustively with the
question of employment efficiency in a fully dynamic context.24 We have
23 For a discussion of returns to scale in the printing industry, see Rosse (1970).
24 David Card has pointed out that alternative wages may exert a negative contem
poraneous influence on employment even in the absence of Pareto efficiency if firms
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EMPLOYMENT CONTRACTS S85
made some attempt, however, to allow for a lagged response of employment
to wages by placing our employment equations with a partial adjustment
model that includes lagged values of the endogenous variable on the righthand
side. With this amendment, we find no serious evidence of remaining
serial correlation in the residuals from our estimated equations. Obviously,
however, our model for the time-series properties of the data can be questioned.
Although our major results do not appear to be sensitive to our
treatment of the dynamic nature of the data, the reader should be aware that
we think there is some ambiguity regarding the appropriate way to deal with
this issue.
The Issue of Identification
Our discussion in Section III focused on the implications of Pareto efficiency
for employment determination and confined its attention to equations such as
(19) and (22), in which employment is treated as a function of the contract
wage. In the bargaining context that we have stressed, however, it is almost
certainly true that contract wages and employment are jointly endogenous,
and so the question naturally arises, Are equations such as (19) and (22)
identified? As usual, the answer to this question depends on the assumptions
one is willing to maintain.
To pose the problem in its simplest form, suppose that bargaining between
the firm and the union leads to a contract wage that is some linear function of
workers' marginal revenue product and their alternative wage, for example,
w = do + dLRL + d2w. (B6)
Suppose also that efficiency condition (1 1) leads to an employment equation
of the general form
RL = go + glw + g2w. (B7)
If equations (B6) and (B7) describe the determination of contract wages and
employment, it is apparent that neither equation can be identified without
further restrictions.
In the absence of any other information, in order to identify equation (B7),
we seek some variable(s) that will influence the wage bargain (B6) without at
the same time influencing the efficient level of employment (B7). Unfortunately,
none of the standard variables typically used to identify labor demand
and supply functions will work in this case, since equation (B7) incorporates
all variables influencing both supply and demand. Our choice must be limited
to only those variables that affect unions' wages independently of the optimal
employment of union members.
After considering a number of possibilities, we have concluded that our
best hope for identification lies in the presence of contractual arrangements
that are designed to stabilize workers' earnings over time or to compensate
workers, ex post, for price-induced changes in the purchasing power of their
earnings. With income-smoothing arrangements, one might expect equation
(B6) to include lagged wages as well as current values for RL and w. If so and
if there were no corresponding lags in the effects of contract wages on
efficient employment, lagged wages could serve as instruments in the estimaface
nonzero costs of employment adjustments and if future contract wages depend
positively on current alternative wages. For a careful treatment of employment
efficiency in a dynamic context, see Card (1984).
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S86 JOURNAL OF POLITICAL ECONOMY
tion of equations such as (B7). A similar argument might be made for arrangements
that index current wages to some average of current and past
consumer prices. In this case, current and past consumer prices would enter
equation (B6) but would enter equation (B7) only insofar as they directly
influence optimal employment levels. For the printers in our sample it seems
reasonable to assume that the direct employment effect of consumer prices is
negligible relative to the direct effect on wages, and so we have also used
current and lagged consumer prices, in addition to lagged contract wages, as
instruments for current contract wages in the estimation of our employment
equations.25
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