The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to Journal of Political
Economy.
http://www.jstor.org
Testing between Competing Models of Wage and Employment Determination in Unionized
Markets
Author(s): Thomas E. MaCurdy and John H. Pencavel
Source: Journal of Political Economy, Vol. 94, No. 3, Part 2: Hoover Institution Labor
Conference (Jun., 1986), pp. S3-S39
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/1837175
Accessed: 18-03-2015 10:33 UTC
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
http://www.jstor.org/page/info/about/policies/terms.jsp
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content
in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship.
For more information about JSTOR, please contact support@jstor.org.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
Testing between Competing Models
of Wage and Employment Determination
in Unionized Markets
Thomas E. MaCurdyand John H. Pencavel
Stanford Universityand National Bureau of EconomicResearch
Two models of wage and employment determination in unionized
markets are routinely exposited. According to one, wage and employment
outcomes are on the firm's labor demand curve; according
to the other, wages and employment are on the parties' contract
curve. This paper spells out an empirical procedure that discriminates
between these two models and applies this procedure to the
particular case of the newspaper industry and the International Typographical
Union. The labor demand curve model is inconsistent
with our data, while the contract curve model comes closer to describing
our observations.
I. Introduction
The existing literature in economics on the determination of wages
and employment in unionized markets reveals three general approaches
to the problem. The first approach can be traced to Dunlop's
(1944) seminal work, and it characterizes the union as setting the
wage rate to satisfy some objective while the firm responds by deterWe
are grateful to Cathy Hartsog and Sarah Lane for their conscientious research
assistance. We have also benefited from Andrew Oswald's comments on a preliminary
draft of this paper, from Henry Farber's comments on a later draft, and from many
conversations with James Rosse, who possesses a remarkable knowledge of the newspaper
industry. Our work has been supported by grants from the National Science Foundation
to the National Bureau of Economic Research (NSF grant no. SES 83-08664)
and from the Sloan Foundation to MaCurdy and to the Department of Economics at
Stanford University. Pencavel also received support from the Center for Economic
Policy Research at Stanford University.
[Journal of Political Economy, 1986, vol. 94, no. 3, pt. 2]
(?)1986 by I[he University of Chicago. All rights reserved. 0022-3808/86/9432-0005$01.50
S3
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S4 JOURNAL OF POLITICAL ECONOMY
mining employment according to its labor demand function. Dunlop
himself suggested the wage bill as the relevant objective for the union
in many circumstances, and it was Fellner (1947) and Cartter (1959),
among others, who generalized this to an ordinal objective function
involving the wage rate and employment. This approach has had
considerable appeal to labor economists because most American collective
bargaining contracts appear to grant management considerable
discretion over matters concerned with employment.' Also, because
the position and shape of the labor demand function are the
ultimate constraint on trade union behavior, it is well suited to Marshall's
(1920) and Friedman's (1951) conjectures about the effects of
different types of unions on relative wages, and it lies behind Lewis's
(1963) well-known estimates of the relative wage effects of unionism
from 1920 to 1958.
This is a conventional model of a monopolist's (the union) setting
prices and a buyer's (the employer) reading off his quantities to be
purchased from his demand curve. As is the case when price-setting
power is exercised on only one side of the market, the wageemployment
combination determined by this model lies off the contract
curve (save for pathological cases) and, as such, runs counter to a
respected tradition in economics that is strongly disposed toward outcomes
in which such unexploited gains to trade do not exist.
A second approach to modeling union-management behavior,
therefore, yields wage and employment contracts that are Pareto
efficient. This approach can be traced to Edgeworth's (1881) model of
bargaining and to Bowley's (1928) bilateral monopoly, and, as Leontief
(1946) demonstrated, such an efficient solution may result when a
union presents management with an "all-or-nothing" wage and employment
combination. Although the emphasis placed on self-interest
often inclines economists toward disregarding all inefficient solutions,
it should be noted that the standard of efficiency used here is one that
neglects the transactions costs of negotiating an agreement. In fact,
the collective bargaining process is one in which, through threats and
guile, each party attempts to conceal its true valuations from the other
party, and in such circumstances whether or not the Pareto frontier
(defined as excluding these negotiating costs) is attained should not be
presumed but should have the status of a testable hypothesis.
These two approaches to modeling union-management behavior
present determinate solutions to the bargaining problem but are silent
about the process by which these solutions are reached. Put dif'
A perusal of the four most popular American undergraduate labor economics
textbooks finds this approach exposited in three of them, while the second approach is
not presented in any of them.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S5
ferently, they specify the characteristics of the final outcomes yet say
nothing about the convergence over time of a sequence of offers and
counteroffers on the part of the union and management. It is toward
remedying this neglect of the time-dependent bargaining process that
the third approach to modeling union-management behavior is directed.
This approach is identified with the work of Zeuthen (1930),
Hicks (1932), Cross (1965), and others who drew attention to the
formation of each party's expectations about the other party's behavior
and to the costs imposed on each party as time passes without
agreement having been reached. The problem with the work in this
approach has been that a well-defined contract is not normally determined
unless certain (unappealing) asymmetries or arbitrary learning
assumptions are imposed on the behavior of the bargainers.2 Hence,
while a bargaining model providing a characterization of the dynamic
sequence of negotiating moves and concluding with a determinate
agreement would considerably enhance our understanding of collective
bargaining, no satisfactory model of this type exists at the moment.
Consequently, this paper focuses on the first two approaches to
wage and employment determination.
The purpose of this paper is to specify for each of these two approaches
the particular solutions for the employment contract and to
implement them empirically in such a way as to determine the relevance
of the one or the other approach in a given labor market setting.
Although our procedures could be implemented with data from
a number of different labor markets, in this paper we take up the case
of the American newspaper industry and its primary labor union, the
International Typographical Union (ITU). This choice was determined
by several factors. First, the institutional characteristics of the
newspaper industry and the ITU render it particularly suitable for an
analysis of this sort. These characteristics are spelled out in Section III
below. Second, the issue of employment determination has been a
recurrent issue of contention between newspaper owners and the
union, the employers charging the union with "featherbedding" practices
and the union describing them as "job security" provisions (see
Porter 1954). Third, the industry's and the union's publications provide
an unusually rich source of detailed data that permit the construction
of variables corresponding closely to their theoretical concepts.
Fourth, both the technological conditions of newspaper
2 For example, in Cross's (1969) highly original model, at every round of the negotiations,
each party assumes that he will not make any further concession, and yet, after
having investigated his opponent's offers, each party revises his negotiating position. In
Coddington's (1970) words, "each bargainer always trusts himself to stand firm in spite
of an unbroken record of failures to do so in the past. Self-deception is rife for each
bargainer learns something about the other's behavior but nothing about his own."
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S6 JOURNAL OF POLITICAL ECONOMY
production and the issue of wage and employment determination of
typographers have already been the subjects of investigation by economists
(see, e.g., Rosse 1970, 1977; Dertouzos 1979; Dertouzos and
Pencavel 1981; Pencavel 1984a, 1984b), so there exists a body of research
findings on which our work may build.
The following section specifies the objectives assigned to the union
and to the firm, and it formalizes the two approaches to determining
wages and employment with which this paper is concerned. Section
III describes the critical institutional features of the ITU and of the
American newspaper industry and introduces the data that are used
in the empirical work. The results from this work are presented in
Section IV, and conclusions are drawn in Section V.
II. Alternative Characterizations of
Union-Management Contracts
A. The Objectives
The trade union is characterized as behaving as if it possesses a twice
continuously differentiable, strictly quasi-concave, ordinal objective
function
U = ti p- , L, wp), (1)
where w measures the money wage rate, p is the price level of commodities
consumed by the workers, L is union employment, and wa
represents an alternative wage rate or a wage index that may be
relevant to the union when determining its employment and wage
choices.
The first partial derivatives of this function with respect to wip and
L are assumed to be strictly positive. Following Leontief (1946), Fellner
(1947), and McDonald and Solow (1981), a graphical analysis
helps to clarify the difference between the models, and so we graph
the indifference curves between w and L associated with the union's
objective function in figure 1. The union is assumed to produce such
a small fraction of the economy's total output that it may disregard
any effect of its decisions on the overall price level, p. This objective
function is "the" union leader's, who is assumed to integrate the welfare
of all the union's members. This finesse of the well-known problems
in aggregating over individual utility functions appears slightly
less heroic in the particular case of the ITU in view of the fact that
"from a socio-economic point of view [it] is as homogeneous as any
group of that size could be" (Lipset, Trow, and Coleman 1956, p.
309).
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S7
w
U0
U2
U3
O L
Fi;(. 1. The union's indifference map
As for the newspaper firm, it is convenient to characterize it as
producing n + 1 different dimensions of output, with the level of
output of each given by X, Y1,. . ., YW Here X represents output from
the composing room of the newspaper, which is that stage of the
production process in which typographers work. We posit for the
firm a very general objective, namely, the maximization of the function
V:
V = f(X, YI. Y,7, C, CO), (2)
where C denotes the costs incurred in producing X, COstands for all
other costs, and different product market conditions imply different
expressions forf. Function V is assumed to be strictly increasing in X
and in each YKand strictly decreasing in C and C,. The costs from
operations in the composing room are given by C = wL + IRKI,
where L represents the number of typographers employed, w their
wage rate, K, the level of input i used, and R, the given rental price of
one unit of input i. This objective function, equation (2), is consistent
not merely with conventional cost minimization and profit maximization,
but also with certain "managerial" theories of the firm. The
advantage of writing the firm's objective in this fashion arises from
the fact that the typographer's work in the composing room represents
one stage in the chain of a newspaper's production, and, while
the composing room's output is not explicitly sold to the stereotyping
room and to the pressroom, the integrated newspaper firm nevertheless
places a corresponding implicitvalue on the output from the
composing room. Under conditions that will become evident, our
analysis may focus exclusively on the activities of the composing room
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S8 JOURNAL OF POLITICAL ECONOMY
or, equivalently, on the behavior and technology involved in producing
the output X.
Suppose that changes in the employment of typographers and of m
other inputs affect the composing room's output X through a conventional
production function X = X(L, K1, ... , KM)Y1,. . . mY), where
Y., . . ., Y, represent intermediate inputs produced by other components
of the newspaper that are needed to produce X. With this
specification of X(-), changes in L or in the Kj's affect V or the
profitability of the firm only through their impact on X. The equation
defining combinations of w and L that yield the same value of V
(i.e., the firm's indifference curve) is dwidL = - [(aflaX)(aXlaL) +
w(aflaC)]![L(aflaC)],which depends on the particular expression for f.
For an important class of objective functions (including profits), the
firm's indifference curves will have the shape given in figure 2-a
positive slope with respect to L until - (aflOX)(aX/aL)= w(aflaC)and
then a negative slope.3 In the graph, V( > VI> V2> V3.The dashed
line Ld connecting the maximum points on each of the indifference
curves denotes the firm's optimal level of employment for given
values of w. In other words, Ld is the firm's labor demand curve.
B. AlternativeModels
According to the first approach to the determination of wages and
employment in unionized markets, the firm selects its optimum use of
labor and other inputs for any configuration of input prices while,
subject to these decisions by the firm, the union sets the wage rate to
maximize the value of its objective function, equation (1). For inputs
used in positive amounts, the firm's first-order conditions for the
maximization of equation (2) are as follows:4
af ax + a =,
aXdaL 1W?
af ax + _(3)
ax aKj + ac Rj 0,
or, combining the two equations,
R axIa )= w. (4)
All equilibrium combinations of w, L, and K9must satisfy first-order
condition (4) so that at all times the firm is on its V-maximizing input
3 See Fellner (1947) and McDonald and Solow (1981) on the shape of the firm's
indifference curves when it maximizes profits.
' For both models of wage and employment determination, the second-order conditions
for a maximum are assumed to be satisfied.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S9
W Ld
V0
Of~~~~~~~~~~V
0 L
FIG. 2.-The firm's indifference map and labor demand curve (L')
demand curves (though at points different from those that would
obtain if there were no union setting the wage rate). In recognition of
this, we designate this characterization of union contracts as the labor
demandcurveequilibriummodel(LDEM). One important special case, of
course, occurs when V represents profits and the firm is always on its
profit-maximizing input demand curves. The LDEM has the property
that all inputs are employed such that, in the production of any output,
the ratio of their marginal products equals the ratio of the prices,
and it is this property that is exploited in the empirical analysis below.
The union's policy is to set w to maximize equation (1) subject to the
satisfaction of the firm's marginal conditions such as equations (3).5
Equilibrium in the LDEM is defined by point A in figure 3, where Wris
the wage that would exist in the absence of the union. Of course,
insofar as the union sets the wage rate above the transfer price of
labor, then some mechanism such as long apprenticeship programs,
high entrance fees and dues, or nepotism must be adopted to ration
employment among those offering themselves for work. On the other
hand, because employment is always adjusted such that the marginal
value product of labor is equal to the union-determined wage rate,
this sort of employment contract should not be characterized by work
practices such as make-work and featherbedding.
5One way to think of the inefficiency of the LDEM is as the outcome of a standard
principal-agent problem: w and L appear in the objective functions of both parties and
the principal (the union) sets w, but it cannot prevent its agent (the firm) from determining
L according to the agent's own interests.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
Sio JOURNAL OF POLITICAL ECONOMY
W
Ld
A
Wr
O L
FIG. 3.-Equilibrium in the labor demand curve equilibrium model
The second approach to the bargaining problem has the union and
the employer explicitly or implicitly entering into agreements such
that the wage-employment combination lies somewhere on their contract
curve, and, from the point of view of the parties (but not necessarily
of society), the contract is Pareto efficient. We label this the
contractcurveequilibriummodel(CEM). The contract curve is defined by
the locus of the points of tangency between the union's and the employer's
indifference curves as illustrated by the line CC' in figure 4.
The contract curve can take a wide variety of shapes as shown in
figure 5, the relevant shape and range depending on the particular
forms of the objective functions of the union and the firm.6 In some
research, the shape of the contract curve is presumed to take one of
the three possibilities drawn in figure 5, and typically the results of
this research depend crucially on the form of the contract curve presumed.7
By contrast, the empirical work in this paper is consistent
with the contract curve's taking any of the three shapes in figure 5.
The expression for the contract curve may be derived by charac-
6
In fig. 5 we have drawn the contract curves as originating at the wage-employment
combination that would exist in the absence of the union. This arises when the union's
indifference curves are horizontal at wr and when the union's threat point is given by w,.
7 For instance, some authors maintain the hypothesis that the contract curve is vertical.
If this is the case, then a test of whether wages and employment are determined by
the CEM consists in whether the partial correlation between wages and employment is
zero. Unfortunately, a finding that the partial correlation between these variables is not
zero is consistent with the hypothesis that contracts are efficient, but the contract curve
is not vertical. Indeed, this alternative explanation is consistent with our empirical
results below, which reject the special case of a vertical contract curve.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION SI'
w Ld
Wr
0 L
FIG. 4. The contract curve CC'
terizing w, L, and each other input being selected such that the
union's objective function, equation (1), is maximized subject to a
given level of V for the firm's objective function, equation (2). In this
analysis it is important to keep in mind that we are assuming that the
firm operates on (not inside) its production frontier. As before, with
changes in the employment of typographers and of another input j
d
W
C2
0 L
FIG.5. Alternative contract curves
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S12 JOURNAL OF POLITICAL ECONOMY
affecting V only through the production of X, the first-order conditions
for CEM include the following:
g,, P= aC L,
of AX - o- _f
_ ax -_ Rj
where g,,, = aU/l(wlp) > 0, gj = aUh3L> 0, and Xis the Lagrange
multiplier, which is equal (at the optimum) to the slope of the payoff
frontier. Using the first two equations to eliminate Xand combining
this expression with the third equation yields the relation
R-X/
a I =w - pL , (5)
Because the term pLg~igo is strictly positive, inputs are not being employed
such that the ratio of their marginal products equals the ratio
of their input prices; instead, labor is employed such that the marginal
product of labor to the marginal product of inputj falls short of
the ratio of the wage rate to the price of input j. Expressed differently,
the union is obliging the firm to employ more workers than it
would otherwise choose to do at the negotiated wage, and these
"superfluous" workers may be accommodated through minimum
crew sizes and featherbedding arrangements.8 Also, a wage rate in
excess of the transfer price of labor will require some mechanism to
ration employment among those offering themselves for work (just as
in the case of the LDEM). In other words, the CEM will be characterized
both by devices to restrict entry into union employment and by
rules that serve to absorb the excessive number of workers employed
(excessive, that is, given the relationship between marginal products
and input prices). The presence of restrictive work practices, therefore,
is not some haphazard or incidental element of various labor
contracts but rather a distinguishing feature and an integral property
of a particular class of models of wage and employment determination
in unionized markets.
With the structure thus imposed on the problem so far, equation (5)
could be satisfied with a number of different combinations of wage
rates and employment, each combination distinguished by the property
that the welfare of one party can be improved only at the cost of
' Here our use of the term "featherbedding" corresponds to a situation not where the
marginal revenue product of labor is zero but simply where the marginal revenue
product of labor falls short of the wage rate.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S13
some reduction in the other's welfare. To determine which single
combination of these many efficient wage and employment exchanges
will obtain requires the introduction of particular behavioral postulates
that yield specific solutions (such as Nash's proposed solution). It
is important to recognize, however, that equation (5) applies to all
specific solutions of the CEM.
C. Means of Testing theModels
First, let us consider if there exist inclusion or exclusion restrictions
that allow us to determine from equation (5) whether labor market
contracts are efficient. Unfortunately, with respect to each of the
variables wip, L, and WaIP, no such inclusion or exclusion restrictions
are implied unless strong assumptions are imposed on the nature of
union objectives. For instance, w may be included in equation (5) or it
may be excluded: if we were willing to maintain the hypothesis that
the union's objective function is given by U = [(wip) - 8(Wa/P)]L(i.e.,
a form of rent maximization), then w is excluded from equation (5)
and the contract curve is vertical. This objective function also leads to
a situation in which L does not enter relation (5). However, there are
no compelling a priori reasons or persuasive empirical evidence to
assume such a special form for the union's objectives, and so, in general,
neither w nor L is excluded from equation (5). Consider, further,
the role of the alternative wage variable, Wa. Clearly, if Wa is not an
argument of the union's objective function, then Wa is absent from
equation (5). Of course, such a situation does not imply that the negotiated
solution of w and L in the CEM is unaffected by Wabecause the
union's threat point is likely to be a function of this variable. Even if Wa
directly enters the union's objective function, it need not be included
in the first-order condition given by equation (5). As an illustration,
suppose U = 4(L)(W/Wa)J, where + is some monotonically increasing
function of employment. In this case, gL/gw is independent of Wa, and
consequently the alternative wage does not enter the first-order condition
of the CEM considered here. In short, the absence of Wa from
equation (5) does not permit us to infer that employment contracts
are efficient.9 In general, the CEM cannot be tested in a particular
labor market context by determining whether any of the variables wip,
' This conclusion stands in sharp contrast to Brown and Ashenfelter's (this issue)
arguments. They base their empirical work on determining whether wa enters into eq.
(5). They assume that the left-hand side of eq. (5) represents the marginal revenue
product of labor and specify an expression for it. They then explore whether this
expression is correlated with various measures of wa, arguing in the context of eq. (5)
that "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." By contrast, we have argued that the absence of wa from eq. (5) does not
allow us to reject the CEM.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S14 JOURNAL OF POLITICAL ECONOMY
L, and wa/p are either included or excluded from equation (5)-no
such inclusion or exclusion restrictions are implied.
Now let us consider whether exclusive restrictions exist to test the
LDEM. In fact, it is straightforward to observe that equation (4)
characterizing the LDEM is a special case of equation (5) describing
the CEM, namely, the special case in which the term -LpgIlg,,, is
absent. In other words, through a specific exclusion restriction, equation
(5) nests the LDEM as a special case, and, by subjecting this
exclusion restriction to conventional testing procedures, equation (5)
becomes potentially a very fruitful form for discriminating between
the CEM and the LDEM in any particular labor market context. It
should be noted, however, that this procedure will discriminate between
the CEM and the LDEM only if gL > 0 and gtO> 0. Thus, in
terms of figure 1, if the union's indifference curves are horizontal
straight lines (the union cares only about wages and not about employment),
then all wage-employment combinations lie on the labor
demand curve. This illustrates once again the fundamental point that
ultimately a rigorous test of the CEM depends on the specification of
the union's objective function.
Observe that both models have been set up in such a way that they
describe the newspaper firm's behavior within any given stage of the
multistage process of producing a newspaper, and for their application
equations (4) and (5) do not require information on outputs or
factor inputs in other stages. This is important because typographers
(the labor represented by the ITU in the union locals used in our
empirical analysis) are employed at one such stage, namely, in the
work undertaken in the composing room, so the relevant marginal
products in equation (5) relate to the production technology within
the newspaper's composing room. We turn now to consider the
specification of the composing room's production technology and also
to describe the critical institutional features of the ITU that affect the
appropriate form for the union's objective function.
III. The Institutional Setting
The data used in this paper to test between the LDEM and the GEM
consist of annual observations on wages, employment, and other variables
describing the members of the ITU and the daily newspapers
for 13 American towns in various years from 1945 to 1973. These
data were compiled for this particular study and are a different set of
ITU locals from those used in previous analyses of this labor market.10
The major data problem relating to this industry has always
10
The data collected by Dertouzos (1979) and used in Dertouzos and Pencavel (1981)
and Pencavel (1984a, 1984b) form the basis of the observations also used by Brown and
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S15
been the generation of an accurate series on the employment of typographers
in the production of newspapers. In previous work, this
problem was handled by not using observations on very large cities
(such as New York, Boston, and Chicago) that have major book and
job establishments so that the local ITU membership data were likely
to be dominated by ITU members working in newspapers rather than
those employed in commercial (book and job) printing establishments.
Further investigation of this issue by James Dertouzos of the
Rand Corporation, who has corresponded with a number of ITU
locals, indicates that the association between local ITU membership
and newspaper employment is closest for the smallest locals. For this
reason we restricted ourselves in this study to such locals and compiled
a new data set for these locals only. These locals are listed in
table 1, and their membership (L) ranges from a high of 59 for
Pittsfield, Massachusetts, to a low of 21 for Boone, Iowa.
Table 1 also provides information on the mean values of the other
variables that differ across union locals used in this study. Variables
K, and K2are, respectively, the number of typesetters and teletypesetters,
which constitute the capital inputs used in the composing room
of the newspapers listed, while X denotes each newspaper's annual
advertising linage sold. The hourly contract wage (w) for our sample
of observations averages $2.62, although the range is almost $1.00from
an average of $2.16 for Salina, Kansas, to $3.12 for Butte,
Montana. This illustrates the considerable variation in typographers'
wage rates across cities, and a full explanation for this variation for a
group of workers with very similar skills and other characteristics
from city to city has yet to be provided. The difference between the
real hourly wage of typographers and the real hourly earnings of
production workers in the durable goods manufacturing industry is
given in table 1 by the column headed (w - w)/lp. In all cases, the
typographers enjoyed a wage premium over that received by workers
in the durable goods manufacturing industry, although the size of
that premium varied across cities.
The characteristics of the ITU make it an almost ideal union for the
purposes of a study of this kind. The structure of the ITU is highly
decentralized, and collective bargaining takes place at the local level.
A national or regional minimum wage has never been established,
and in any year there exists the opportunity for the researcher to
construct a number of observations on many different bargaining
Ashenfelter (this issue). These data cover both very small union locals and mediumsized
locals, and previous analysis found significant differences in the objective functions
between these union locals. Moreover, James Dertouzos has advised us that he
believes some of these observations may contain serious measurement errors. For these
reasons we collected a completely fresh data set and restricted it to relatively small
union locals.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
l ) C,C:
in
C- t
. 't.
- - C) in
Cr;C C)
S >'C
X~~~~-S <C'~~~.c~~.c cr) 3 3 =
Cl
C O C-l X0 C-A O) C-A in C-4 C-l C-A C-l C) - .>
0)X )O X C)a) -,I }c O C-l s.c- z C b
C- CA C- C- cn N n r . . C : WC LSo
t- C C)o C4c.c c c1
z i N in i z CO _
C1C -4C -4C 14 cl C l
CM c liClM c lC
C
CCM,C-4 C-4 a. b
CL C
z X SC'JD lCl X O - ,I, CA X-t-> ~ ~~~~ C) ) oo In CA 11 rr
O-
o
X-<
- 00 -X ?
- k~~~~~0000Cl~~~~~~~~l~~~t-~~~~0Cl~ ~ ~ ~ C
0 Cj in O O c C)X in X- cn C
0 O O C'i CCi C-A C,) C - C X 3
cr~~~~ ~~~~~~~~~~C C:
- X X 1- t. C)O X X C-l t- - "I,
ta~~~~~~~~~~~~~~~~C4 (15, tv 3
m -.0 -As X X Csl t-X > C s~~~~~~-_,
,I cn X-dXn :-?)(1-Xtc X< if) <;>C4 ?? 3 f L
0.
cA
CA CACA C CA C C4 CS
4 1 Q_>
H H~~~~~~~~~~~~~~~~~~~~~~~~ci
~ ~ Cz
K z r s o x s - s t ~CI)xEm ; ??
r
d C
H _ _ n; > _ rz crz - ~ ~? f; t D U = r
z 712 * z
0 ~~~~~~~~~~~~~~~~~ C~~~~~~~~~C
z /0~~~~~~c CZ-
adC~
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S17
units. The ITU is a highly democratic union in which many members
have occupied some union office at one time and in which a large
fraction of the membership participate in elections and referenda on
a number of different issues. Moreover, there are no important skill
differentials within the union.11 Consequently, there is no compelling
case in the ITU's objective function for distinguishing between the
interests of the union leadership and of the rank and file or between
the interests of different groups within the rank and file.
As we have already noted, our analysis assumes production to be
efficient; that is, production takes place on and not within the production
frontier.'2 This may not be an innocuous assumption according
to some interpretations of the effects of the ITU's control over employment
and conditions of work. The regulation whereby a standard
advertisement carried nationally is "unnecessarily" reset by union locals,
a so-called bogus rule, has received special attention, although
the extent to which practice actually conforms to this rule is uncertain,
and it is likely to be of little consequence for our work with small
newspapers. The reasons for this are twofold. First, for the very small
newspapers in our sample, national advertising represents no more
than 10 percent of all advertising linage. Second, the procedure is
such that the bogus rarely gets set. The items awaiting to be reset by
the bogus rule are put aside until work slackens and there is ample
time to attend to it. According to the jargon, the bogus material sits on
the "hook." There are local rules about the length of time that bogus
material sits on the hook-sometimes 1 month, sometimes 3 months,
sometimes 6 months-before being destroyed. It is not unusual for
bogus material to be destroyed without ever being reset. Moreover, it
may well become a bargaining chip between the management and the
union whereby the union will ask for a few cents more on the contract
wage in return for destroying the inventory of bogus on the hook. In
other words, the employer buys out the bogus.
The Taft-Hartley Act notwithstanding, the ITU operates a closed
shop whereby all individuals hired for work in the composing room
are drawn from the pool of union members. Its concern with the
employment effects of new technology is well known, and, indeed,
today its very existence as an organization of highly skilled workers
whose lineage can be traced back to the medieval guilds is threatened
by the diffusion of typesetting computers, which eliminate many of
" A fascinating analysis of these characteristics is found in the classic study by Lipset
et al. (1956).
12 Production is thus assumed to be efficient, but we do not assume wage-employment
contracts to be efficient (i.e., to be on the contract curve). The two concepts of
efficiency are quite distinct.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
Si8 JOURNAL OF POLITICAL ECONOMY
the special skills once required for printers.'3 This radically new technology
is not represented in our data set, but other, less drastic,
changes in the composing room's operations did take place during the
period under study.
Newspaper type can, of course, be set by hand, though this practice
largely disappeared during our period of study except for the setting
of some headlines or large display advertising. Otherwise, composition
was by typesetting machine with which a skilled operator can
produce solid lines of leaden words and assemble them automatically
into columns. The next mechanical advance was the teletypesetter,
which requires less attention from specialized labor. Here a worker
uses a keyboard similar to a typewriter to punch copy onto a tape.
This is then fed into the composing machine, which automatically sets
the type. Teletypesetters can be used together with the old typesetters,
and, indeed, there is some anecdotal evidence to suggest that this
combination is desirable (see Rucker and Williams 1969, pp. 76-77).
The next development in mechanical composition, the phototypesetter,
which uses photographic processes, did not make an appearance
for any observations in our sample. As is evident from the descriptive
statistics in table 1, typesetters were far more common to our data set
than the teletypesetters, and, indeed, for some newspapers in the
earlier part of our period, no teletypesetters were used.
According to the technology that dominated our sample of observations,
the news and advertising departments would send their copy
to the composing room, and this copy would be set by machine and by
hand and assembled in steel chases (frames). After proofing and
"making up" (i.e., the final reorganization to adjust the various news
and advertising items to fit each page), the chases would be sent to the
stereotyping room in the case of newspapers with larger circulations
or straight to the pressroom in the case of smaller daily and weekly
newspapers. The activities of the composing room, therefore, represent
one step in the multistage process of producing a newspaper so
that, if Y, represents the copy or output of the news and advertising
departments, then the composing room's output, X, is produced according
to the function X(L,KI, K2, Ye).Because all of Y, is typecast by
the composing room, X is simply proportional to Y., so the relevant
production function for our analysis is simply X(L, K,, K2), and the
model outlined in Section II (as was argued there) may be applied to
the operations within the composing room.
13 The parlous consequences of this new technology for the ITU are illustrated in
Rogers and Friedman (1980).
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION Si9
IV. Empirical Analysis
A. The ProductionFunction
The estimation of the stochastic version of equation (5) requires
knowledge of the marginal products of each of the inputs into the
production of the composing room's output. Therefore, the first step
of our empirical research consisted in determining an accurate representation
of the production technology, and we considered many
specifications. Much of this research involved estimating production
functions of the form
InX = -DJ+ Zo + E, (6)
where D- is a dummy variable taking the value of unity for newspaper
j and of zero otherwise, X is the amount of advertising linage sold
annually, Z is the vector whose elements are known functions of inputs,
the coefficients 13,and (xare parameters, and e is an error term
representing the effects of omitted variables. To carry out this empirical
analysis of the production technology we employed a comprehensive
data set consisting of outputs and inputs associated with composing
room activities for 13 newspapers for various years between 1945
and 1973.'1
Extensive work was undertaken on investigating alternative functional
specifications of the production relationship. We started by
considering a simple Cobb-Douglas technology after allowing for
fixed differences between the 13 newspapers. In particular, in terms
of equation (6), we set Z = [ln(L), ln(KI + 1), ln(K2 + 1)] and (x' =
(Oa, a 1, ai), where L is the number of typographers listed as members
of the ITU local, and K1 and K2 (i.e., the number of typesetters and
the number of teletypesetters) are the capital inputs used in each of
the newspapers' composing rooms. (Mean values for the whole sample
and for each city for these variables are given in table 1.) Perhaps
the most important omitted variable in this specification of the production
function is some measure of the hours worked by the typographers
in the composing room (although, of course, systematic difThe
period from 1945 to 1973 allows for a maximum number of annual observations
of 29 for each union local. In fact, as is evident from table 1,the largest number of
observations on any union local is 27 for San Luis Obispo. The reason for not having 29
observations is simply that we encountered missing data on the reporting of mechanical
equipment in particular years, and occasionally ITU contracts for certain locals were
not reported. Also, we deleted all observations for which photocopiers served as an
input in the composing room to avoid having to deal with structural shifts arising from
technological change.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S20 JOURNAL OF POLITICAL ECONOMY
ferences in hours worked across newspapers will be accounted for by
the coefficients 1 in [6]). Data on "normal" weekly hours (i.e., the
number of hours before overtime rates apply) are available, but information
on actual hours worked could not be located. Otherwise, equation
(6) includes the primary determinants of composing room output.
We would have preferred using total linage as our measure of
output, but we were unable to obtain complete data on news linage, so
we assume that total linage is proportional to advertising linage,
where the factor of proportionality varies from firm to firm. The
firm-specific intercepts 1 in equation (6) account for these factors of
proportionality.
The consequences of estimating equation (6) for this Cobb-Douglas
specification of Z and (x yield coefficient estimates as follows (with
estimated standard errors in parentheses):
&l = .730; &, = .489; and&2 = .082.
(.146) (.284) (.038)
The estimation technique here is instrumental variables, where the
instruments are given by the dummy variables (D.)and the interaction
of these dummy variables with linear and quadratic time trends.'
Because it is not reasonable to assume that observations are independently
distributed over time for the same newspaper, one cannot use
conventional formulae for calculating standard errors in instrumental
variable estimation. The Appendix to this paper gives the precise
details of the estimation procedure and the computation of standard
errors implemented in this analysis. The standard errors reported
here are computed in a way to be robust against heteroscedasticity
and autocorrelation up to the third order. These estimates of the
production function coefficients are consistent with what is known
about the technology of the composing room, and, indeed, the increasing
returns to scale that our point estimates suggest (&,j + &, +
U2 = 1.30 1) are a well-known feature of the entire newspaper production
technology.' 6
It is important for our testing procedure that an accurate characterization
of the marginal rate of substitution among inputs in production
be determined, and the Cobb-Douglas specification is, of
course, a very simple representation of production technology.
Therefore, we went to considerable lengths to determine whether a
1
'Very similar estimates were derived using a different set of instrumental variables,
namely, a set including the dummy variables (D,) and all the terms making up a fully
interacted cubic in variables measuring retail sales and the number of households in a
given year for a given city.
l' When a time trend is added to eq. (6), the coefficient estimates of (XL, o. 1, and (2 are
virtually unchanged.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S21
less straightforward representation was more appropriate for the
composing room's output by estimating numerous forms of the production
function. These included the transcendental logarithmic
(translog), restricted forms of the translog, the quadratic, the BoxCox
transformation applied to all inputs and output, the transcendental,17
the generalized Stone-Geary (which nests the constant
elasticity of substitution function), and elaborate splines that allow the
form to vary in different regions of the production function. The
estimates corresponding to several of these production functions appeared
at first sight to be satisfactory, but in ascertaining whether they
implied an economically meaningful technology, we determined
whether the fitted values implied (a) diminishing marginal returns to
successive applications of a single input (with other inputs held fixed
at their observed mean values) and (b) positive marginal products at
the levels of the inputs actually used. Although for some of the estimated
production functions these criteria were satisfied for a large
number of observations, they were not met for every single observation.
The explanation for this appears to be that the estimates of the
production functions were unduly affected by combinations of inputs
that represented outlying observations.
However, we were anxious not to impose too restrictive a form of
the production technology onto the next stage of our estimation procedure.
Therefore, even though for some observations the estimates
of the translog production function do not meet the two criteria
specified in the previous paragraph, we also present results corresponding
to a more general production function, the translog. This
means in terms of equation (6) that
Z = {ln(L), ln(KI + 1), ln(K2 + 1), [ln(L)]2, [ln(Ki + 1)]2,
[ln(K2 + 1)]2, [ln(L)] * [ln(Kj + 1)],
[ln(L)] * [ln(K2 + 1)], [ln(Kj + 1)] * [ln(K2 + 1)]}
and
at = (OtL, Ot1, ?t2, OtLL, (xI1, ?t22, OtL1, OtL2, Ot12),
where, as before, L represents employment, K1 the number of
typesetters, and K2 the number of teletypesetters. The estimates of
this translog production function (with estimated standard errors in
parentheses) are as follows:
&j= -2.130; &1 = 8.337; &2 = .4O7;&LL = -.372;
(1.499) (3.686) (.473) (.617)
17 By transcendental we mean X = A:5Z? exp(biZi), where a, and bi are parameters
and Zi denotes the level of input i.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S22 JOURNAL OF POLITICAL ECONOMY
&1l = -3.591; &22 = *014;&L1 = 2.448;&12 = .072;
(1.074) (.079) (1.383) (.142)
&12 = - .263.
(.258)
Again, these are instrumental variable estimates, where the instruments
are the newspaper dummy variables (D>)and the interaction of
these dummy variables with linear and quadratic time trends. As
before, the computation of the standard errors takes account of thirdorder
serial correlation and heteroscedasticity. For the next step in
our procedure, we make use of estimates of both the Cobb-Douglas
and the translog production functions.
B. A Specificationfor Union Preferences
The subsequent empiricalanalysisassumes that gL/gw, the marginal
rate of substitution (MRS) function associated with the union's objective
function g(Q),is given by
9gL m (7)
g@ m2
with
M- = Silj + Bi2 + -O pa 012L; i = 1 2,
where Aii, I (dill 0)i2, and 8 are parameters assumed to be constant
over unions and time, B is a dummy variable that takes a value of one
for the three largest unions in the sample (i.e., locals 163, 126, and
109) and of zero otherwise, wa is a wage index representing the alternative
wage rate measured here by the real average hourly earnings
received by production workers in durable goods manufacturing, and
L represents employment. Setting one of the [uyl'sor 0-'s equal to one
represents an arbitrary normalization and is needed to identify the
remaining parameters when carrying out estimation.
Many familiar objective functions imply a specification for the MRS
that is a special case of (7). In particular, setting 0 11 = 022 in (7) yields
a specification consistent with any monotonic transformation of quadratic
preferences given by
U = ,1L ? gU2(- - pW)?+l(W )Lp p
+ O22L 2? ( - 8 pa)2
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S23
where the parameters [LIand [2 are defined as 1i = I1and P12 = 22
for a relatively small union and as ,uI = [L1I + [L12 and [2 = [L21 + [L22
for a union classified as large in our sample. With 012 = 021 = 0 and
022 = I in (7), we obtain the MRS corresponding to monotonic transformations
of a Stone-Geary preference function given by
U =
Oil
+ (w _ a, Wa G] + L)
"''
If we specialize this Stone-Geary function even further by imposing
the additional restrictions [LI I = P412 = [L21 = 22 = 0 and 0 = 1,
then the union acts to maximize rents given by
U = bW 8 WEL.
Up p
Hence the specification for the MRS considered here admits a wide
range of possible objective functions characterizing union prefer-
ences.
C. FormulatingtheBasic EmpiricalRelation
To complete the development of an estimable specification for the
equilibrium conditions associated with either the LDEM or the CEM,
we require a measure for the firm's marginal valuation of labor
(MVL) given by
MVLR~*ax ax_MVL=
3R . 3K,=R.Q
MVLRiaL /aK -I * i
which, of course, equals the marginal revenue product of labor when
the firm is a profit maximizer. For the specification of the production
given by (6), the marginal rate of technical substitution Q,between the
inputs L and Ki equals
dZ2
Q1 = J z1 , =1,2, (8)
aKi I
where is the number of elements in the vectors Z and (x,and Z, and
cv,j = 1,... ,J, are the jth elements of these vectors. For a measure
of the rental price of capital input i, we assume that Ri is proportional
to an annual user cost of capital given by the quantity
R _(PMl 2-PM2 )(r + b),
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S24 JOURNAL OF POLITICAL ECONOMY
where PM1 and PM2 are the price indices for all machinery and
equipment used in manufacturing and for electrical machinery and
equipment, respectively, r is Moody's Aaa domestic corporate bond
rate, and b is an annual depreciation rate set equal to 0.1 in this
analysis.'8 Thus we have Ri = yKR,with y, representing a timeinvariant
factor of proportionality that is constant across firms. Combining
results, we obtain MVL = -yRQI.
According to condition (5), equilibrium in the CEM implies
wyRQI= w -pL ml, (9)
which holds for each type of capital input K, employed in the composing
room in conjunction with typographers. Because typesetters are
used at positive levels for all observations while teletypesetters are not
employed by newspapers for some or all years (which indicates corner
solutions for this input during these years), we consider relation (9)
for only the case of typesetters with Q, = Q,.
Throughout this discussion we have implicitly assumed that the
number of hours worked by each employee and union member is
fixed and, thus, can be ignored as an argument of either the union
preference specification or the production function. The interpretation
and the validity of relation (9) continue to rely crucially on maintaining
this assumption. The wage rate in this relation is measured in
terms of dollars per hour, while employment is in terms of number of
workers. This apparent discrepancy, however, creates no conceptual
difficulty as long as typographers work the same number of hours
both across unions and over time; the parameters of the union's preference
and the firm's production functions implicitly translate employees
into hours worked and vice versa. In addition to employment
we would have liked to have modeled the determination of hours per
employee, but we are not aware of any data available on hours actually
worked by typographers.
Our empirical analysis estimates an equation based on a stochastic
variant of relation (9). Suppose that union preferences depend on an
unobserved random disturbance v that varies both across unions and
18 The price indices and the corporate bond rate are taken from issues of the Survey
of CurrentBusiness. The value of the depreciation b assumed in our analysis was suggested
by our colleague James Rosse, who has extensive personal and professional
knowledge of the newspaper industry and typographers. For the term r + b to represent
a cost of capital, it is necessary to interpret bas accounting for the physical depreciation
as well as the financial depreciation of capital. We considered other values for b
covering a fairly wide range in our empirical analysis, and our results were not sensitive
to the choice of b. For b = 0.1, which is the value used in obtaining the estimates
reported below, the variable R has a sample mean equal to 11.94, a standard deviation
equal to 3.62, and minimum and maximum values of 5.48 and 20.4.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S25
over time. This is introduced by replacing the parameter [L11 in
specification (7) and determining the function m1by the quantity [I
- v. Multiplying both sides of (9) by m2/pLyields
(y 2pM)m2 m = v, (10)
where we have specified this relation with typesetters serving as the
capital input (i.e., i = 1), and we have suppressed the subscript on y
for convenience.19 For most specifications estimated below, this equation
is nonlinear in parameters, and, consequently, we treat (10) as a
nonlinear simultaneous equation in our empirical analysis with all
variables appearing in this equation considered endogenous.20 Besides
y, other parameters determining union preferences enter this
equation through the functions ml and m2as given by (7). Inspection
of (8) also reveals that the coefficients a of the production function
are present in equation (10) through Qi, but we do not treat these
coefficients a as parameters when estimating (10). Instead, using the
estimates & obtained from our empirical analysis of the production
function described above, we compute Qi based on formula (8) setting
(xequal to &and then substitute Q, for Q'in (10). With this substitution,
a conventional nonlinear two-stage least-squares (2SLS) procedure
applied to equation (I10)-interpreting Q, as simply an observed
endogenous variable-produces consistent estimates for y and for the
parameters of the union's objective function, though adjustments are
needed when computing standard errors.
Given the assumptions maintained in deriving equation (10), it is
easily verified that setting ml = 0 and m2 = 1 yields the empirical
relation consistent with the LDEM, whose equilibrium condition is
given by equation (4); that is, the structural equation above nests the
LDEM. In particular, after normalizing one of the coefficients of the
polynomial m2 to achieve parametric identification, a wage and employment
contract determined according to the LDEM implies that
the remaining coefficients of m2and all the coefficients of ml are equal
to zero. We denote the null hypothesis implying the parametric restrictions
yielding ml = 0 and m2 = 1 as Ho.
To understand more fully the conclusions that can be drawn on the
19 There are, of course, many potential sources for the error term v other than
unobserved differences in union preferences as we have assumed here, such as errors
arising from measurement problems or optimization error. It creates no difficulties in
the following analysis to interpret v as being an error from one of these other sources as
long as its expectation conditional on the instrumental variables equals zero.
20 There is no compelling reason for treating the variables p and R as endogenous
when estimating eq. (10), but adding these variables to the other instrumental variables
used in our empirical analysis changes the estimates and the standard errors only
slightly.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S26 JOURNAL OF POLITICAL ECONOMY
basis of a test of the null hypothesis H(, consider initially the implications
of a rejection of Ho. This rejection clearly provides solid evidence
against the LDEM, but it certainly does not establish the veracity
of the CEM. Without introducing strong functional form
assumptions about union objectives (such as presuming that a union
maximizes rents), no rigorous tests are available for establishing
whether a CEM characterizes the determination of wages and employment.
No doubt there are many models of the labor market that
imply parametric restrictions incompatible with Ho. While a rejection
of Ho does not allow one to claim the validity of the CEM, the estimation
of equation (10) does provide some information suggestive about
whether a CEM might apply. With the CEM the relevant model, for
example, one would expect the resulting estimates of the coefficients
of ml and m2 to imply a specification for union objectives that is a
quasi-concave function of w and L.
Now consider the possible conclusions that can be drawn from an
acceptance of Ho. If Ho is indeed true, it is not the case that the LDEM
necessarily applies for two reasons. First, Ho restricts the MVL only to
be proportional to w for all observed values of w and L, and it does not
require that MVL = w as dictated by the LDEM. Thus, if Ho is valid,
the admissible combinations of w and L need not even be on the labor
demand curve. Second, there exist specifications of the CEM in which
the contract curve is the labor demand curve, and for these specifications
the CEM and the LDEM are observationally equivalent and both
are consistent with Ho. Such is the case, for example, when a union
cares only about wages and not at all about employment, which arises
in figure 1 when indifference curves are horizontal lines; in this case,
MRS = mI/m2 = 0 for all combinations of w and L. Thus, even if Ho is
true and wage-employment combinations are known to lie on the
labor demand curve, the CEM may still apply.
D. EmpiricalFindings
Tables 2 and 3 present estimates for the parameters of equation (10)
for eight distinct formulations of the MRS functions, whose specification
is given by (7). Table 2 reports results assuming that a CobbDouglas
production function describes the technology of the composing
room, while table 3 presents an analogous set of results for the
translog production function. Rows 1-3 of these tables list the estimates
obtained assuming that the MRS is approximated by a simple
linear function of the variables wip, WaiP,and L. Rows 4-6 and 7-8,
respectively, present parameter estimates assuming that union objectives
are characterized by three variants of a Stone-Geary preference
function and by two variants of a quadratic specification for preferThis
content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
.
- - - - ^ * * CA
-~~~~~~.: ^ oo.
cn C(, On
r-Xz - t t-C4i
z -
>
. . . o~ o
-~~~~~~~oo6 r- r- rl o
cn
n
cli kn
- .- - z w~~~~~~C
cl- -' stsi c s
- ~ ~~ ~~~~~~% U'- -- It
00 t ct
oo It It ?. cl nM
cog -cl -cM i-l
00 00 r-cto
Q ~~~~~~~~~~~~~~~~~Q
N- - - Jz
m <- 14cM - I
I I
H~ ~~~-- O O
o 'eC Mm C MC --c)()C MC CM4
_ O O O-C-.tw
_ _ _ I _ I I _ _ _~~~~~~~~.o
N9 4- -- 4X-
O- 4- 4- 4N-
: -~ -: :
000000 CCC.,0 0
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
.e I b
cce *1 *T CC crg
Q X g ct r- o -t x
z ~ z . . .
- I I Il
Q~~~~~ - .-- zot
l-
-.--
ce CM IM ce) C4- -I
w o o o o o o ce) U) in 00 s. C4 ce)- S)
~~ ~ ~ CC4ce
t- C 5 7
24 -r e P- )zoc
C C) c) CIACC) c)cl
-- n ci oA o
-0 t- C) 0 C-C) )-C t-C) C) C4 C) oo _' '
_ OO Csl O - O XU) M X q
000000 ~~~~~~~~0000l
- -O O OOlcl
Ol C M_l _) _ C) Cs
cl - lz C -t - X O
C _44 -C4 O
XY CYl
_~~~~~~~~~~c c tc c
4 4 X 4- 4- X4,
z s ce1-A mPce t>
C CCMOMOCVO-O
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S29
ences. (See the discussion above for the restrictions implied by these
various objective functions.) The normalization >21 = 1 is used to
identify parameters in rows 1-3 and 7-8, and the normalization 022
= 1 is imposed in rows 4-6. The constraint 8 = 1 is invoked in rows
1, 4, and 7, while rows 2, 5, and 8 report estimates assuming that 8 =
0. The column designated "Percentiles of MRS" in these tables presents
the 10 percent percentile, the median, and the 90 percent percentile
of the quantities mI/m2computed for each observation in the
sample evaluated at the parameter estimates associated with the
specification under consideration.
All the estimates presented in tables 2 and 3 are computed using
nonlinear 2SLS,2' with city dummies and city dummies interacted
both with time and with time squared serving as instrumental variables.22
As noted above, we use an estimate Q, in place of Q, in the
implementation of the estimation procedure. The calculation of standard
errors reported in tables 2 and 3 fully recognizes that Qi is the
estimated quantity. While this calculation of standard errors does
assume that the disturbances v are distributed independently across
unions and firms, it uses asymptotic formulas that permit the v's to be
heteroscedastic and that allow the time-series observations on v for a
given union and firm to be freely autocorrelated up to at least the
third order. Admitting this autocorrelation is particularly important
in the current context because one would not expect the unobserved
components of a particular union's preferences that are captured by v
to be uncorrelated from one year to the next. The exact formulas
used to compute standard errors and a briefjustification for their use
are given in the Appendix of this paper. We consider these standard
errors to be very conservative because they are about three to five
21 The parameterization of eq. (10) used to obtain estimates of the coefficients of the
Stone-Geary specifications reported in rows 4-6 is given by
RQl - W
m2 + 'ml = v*. (*)
pL pL
This reparameterization is obtained by multiplying eq. (10) through by the coefficient +
- l/y. Given the functional forms of ml and m2 implied by a Stone-Geary objective
function, a nonsensical global minimum for the conventional nonlinear 2SLS metric
can be readily shown to exist by setting y = [l = 112 = [21 = [-22 = 8 = ? and 011 =
1. While applications of the estimation procedures with the Cobb-Douglas production
function were able to avoid this portion of the parameter space, difficulties were encountered
in the translog case. The use of structural equation (*) rules out this nonsensical
global minimum and, thus, avoids computational problems. The estimate yand its
standard error sYreported in rows 3-6 of tables 2 and 3 are derived using the familiar
asymptotic formulas y = 1/$ and si = y%.
22 As with the production estimates, qualitatively similar results were obtained when
a different set of instrumental variables were specified, namely, a set including city
dummies and all terms making up a fully interacted cubic in variables measuring retail
sales and the number of households in any given year for a given city.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S3o JOURNAL OF POLITICAL ECONOMY
times larger than the conventional standard errors reported by a
nonlinear 2SLS computer routine that makes no allowance for
heteroscedasticity or serial correlation of the disturbance or for estimation
error induced by use of the estimated quantity Q, in place of
Ql
23
We may draw three main conclusions from the estimates of tables 2
and 3. First, these results provide solid evidence against the LDEM.
The parametric restrictions implied by this model (i.e., LII = [L12 =
PL22 = 011 = 012 = 021 = 022 = 0 with normalization[L21 =1 and[I
= 412 = PL21 = >22 = 011 = 012 = 021 = 0 with normalization 022 =
1) are easily rejected at conventional levels of significance for every
specification considered. This finding is not simply an artifact arising
from the imposition of nonlinear restrictions involved in the estimation
of equation (10). Indeed, use of the specifications based on the
linear MRS function to test the LDEM involves nothing more than
determining whether standard exclusion restrictions are satisfied for
these specifications.
As we have already emphasized, in the context of equation (5) there
exists a simple exclusion restriction by which to test the LDEM, but
there are no tests of either inclusion or exclusion restrictions available
for determining whether contracts are efficient. The findings in tables
2 and 3 are generally consistent with more than one set of these
restrictions. For example, the results for the linear specification of the
MRS function with the Cobb-Douglas production function reported
in row 3 imply that each of the variables L, wip, and wa/p enters
equation (10) at conventional levels of significance as determinants of
the MVL, whereas the estimates for the corresponding specification
assuming the translog production function imply that only the variables
L and wip enter this equation.24 Unfortunately, knowledge that
23
As an example, the unadjusted standard errors for the coefficients in row 3 of
table 2 are as follows: .00 15 for 0l I, .000053 for 012, .0037 for LII, .0011 for P 12, and
.031 for B.
24 To test for the relevance of wip, waIp, and L as determinants of the MVL for the
case of the linear specification of the MRS function, write eq. (10) as
W W 0Lv' -p + AlI+ B' 1112 + 011Ip + 0 13 pa + 0 12L = V.
pL. pL p p
The estimates of the 0-coefficients and the associated asymptotic standard errors obtained
with the Cobb-Douglas production function are
01 = .042, 013 = -.026, and 012 = -.0013.
(.0084) (.0058) (.00059)
The corresponding results with the translog production function are
61, = .039, 013= -.015, and 012 = -.0027.
(.0082) (.012) (.00034)
The implied t-statistics associated with these estimates are all well above 2 in absolute
value with the exception of 013 in the translog case, whose t-value is 1.22.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S31
the alternative wage wa/p may not enter equation (10) as suggested by
the translog results provides no information about whether contracts
are Pareto efficient. Naive tests of either zero or nonzero parameter
restrictions using estimates based on an equation such as (10) do not
permit one to argue either in favor of or against the concept of contract
efficiency.
A second conclusion concerns the relevance of the CEM to this
labor market. While it is not possible to perform conventional statistical
tests of the CEM, the results of tables 2 and 3 are generally consistent
with this model. In situations in which this model applies, the
parameter estimates of equation (10) should satisfy certain inequality
restrictions: the parameter -yshould be positive, and, far more demanding,
the estimated relationship obtained for the MRS should
imply a function describing union objectives that is quasi-concave.
The estimates of -yare clearly positive for every specification considered
in these tables. With regard to quasi concavity, the estimates
obtained for the linear specifications of the MRS function in both
tables provide the most obvious evidence supporting this property.
Inspection of these estimates reveals that the MRS is strictly increasing
in wip and decreasing in L. Furthermore, the estimated MRSs for
these specifications are positive for every single observation in the
sample. When combined, these two findings indicate that the underlying
function describing union objectives is quasi-concave over the
range of the data covered by our sample. The results corresponding
to the quadratic specifications imply concave utility functions and
MRS functions that satisfy quasi concavity for most of the relevant
values of wip and L. The results for the Stone-Geary specification of
union objectives are far less supportive of the CEM: a nontrivial fraction
of the estimated values of the MRSs are negative, and the point
estimates in the translog case imply noncredible properties for union
objectives. These latter results indicate that either the Stone-Geary
form of preferences or the CEM is inapplicable. In the light of the
apparent consistency of the CEM when considered in the context of
other preference specifications, we are inclined to reject Stone-Geary
preferences rather than the CEM.
The third conclusion to be drawn from the results in tables 2 and 3
relates to inferences concerning union preferences. There are two
main points. The first concerns the functional form describing union
objectives. Because the linear, the Stone-Geary, and the quadratic
specifications for preferences do not nest one another, it is difficult to
determine which specification best fits the data. As noted above, the
estimated Stone-Geary formulations for preferences exhibit several
disconcerting properties that suggest that such formulations are inappropriate.
With Cobb-Douglas technology assumed, the primary
source of difficulties with properties of the Stone-Geary function
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S32 JOURNAL OF POLITICAL ECONOMY
arises from the large estimates obtained for the "translation parameters"
p.and 8 that define "reference" employment and wages, a situation
that is commonly encountered when such functions are fitted in
consumer demand analysis. In addition to this source of difficulty, the
point estimates of 0ll based on translog technology reported in rows 4
and 6 of table 3 are negative, which is quite implausible and lends
further evidence against a Stone-Geary formulation of union objectives.
Of course, the large standard errors associated with many of the
estimates of the Stone-Geary parameters indicate that considerable
caution should be exercised in rejecting it as an appropriate specification.
As for the linear and the quadratic preference specifications, the
percentiles of the estimated MRS reveal similar trade-offs in equilibrium
between wage rates and employment at the margin. The principal
source of variation in the measured MRS arises from altering
assumptions about production technology, with the estimates of the
MRS higher when the translog production function is assumed. Aside
from the Stone-Geary results in the translog case, the relaxation of
the constraint on the coefficient 8 that determines the influence of the
alternative wage on union objectives produces a value greater than
zero but less than one. This indicates that an ITU local perceives itself
as being worse off if there is an increase in other workers' wages but
would prefer this event to a comparable decrease in its own wage rate.
While there is little basis for choosing among the various
specifications considered in tables 2 and 3, the results of these tables
do provide a clear indication that one popular formulation for union
objectives does not apply for the ITU. In particular, an inspection of
the estimates of the Stone-Geary function and the associated standard
errors offers strong support against the view that these unions maximize
rents; the parameter restrictions implied by rent maximization
are readily rejected at conventional levels of significance.
The second point about union objectives that can be inferred from
the results of tables 2 and 3 concerns the degree to which a union
substitutes between wages and employment. According to the medians
of the implied estimates of the MRSs for the linear and quadratic
specifications, a reduction of employment by one worker may
be offset by an increase in the real hourly wage rate of 3.5-9.5 cents
in 1967 dollars to make the union indifferent to this loss of employment.
The median real wage rate for this sample is $3.01, so this
compensating increase represents approximately a 1-3 percent adjustment
in hourly wages. For a union of size 36-the average size in
the sample-this increase in the wage rate translates into a $2,520$6,840
rise in the total annual real earnings of its 36 members assuming
2,000 hours are worked per year, which compares with a $3.01 x
2,000 = $6,020 reduction in earnings lost, a consequence of one
fewer union member being employed.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S33
Perhaps a more instructive way to interpret this trade-off between
wage rates and employment is to define e as the total rents from
unionization and to write the union's objective function as U = g[(w/p)
- 8(walp),L] = g(eL-1, L), where e = [(wip) - 8(wa1p)]L.Then the
marginal rate of substitution, s, between employment and rents is
given by the following expression:
aU/aL = 1g 1W Wa
s d~lde (g ( p
Now if the union cares only about wages and not about employment
(i.e., if gL = 0), then s = - (wip) + 8(WaIP), while at the other extreme,
if the union cares only about employment and not about wages (i.e., if
g --> oc), then s -> oo.In the special case of rent maximization where U
= [(wip) - 5(WaIP)]L,s is zero. In other words, as the union's indifference
curves between wip and L move from being horizontal to vertical
(in terms of fig. 1), s ranges from a minimum of - (wip) + 8(WaIP)< 0
through zero toward infinity. For our Cobb-Douglas production function
estimates, the average of L(gIg.) for the linear specification of
the MRS function is 1.93 and 8 = 0.62, so the average of s is 0.41. For
our translog production function estimates, the corresponding average
of L(gLlg.) is 2.98 and 8 = 0.39, which implies an average of s
equal to 0.92. These values of s suggest that these ITU locals place
greater weight on employment in pursuing their goals compared with
a rent-maximization objective.
V. Conclusions
Two models describing the determination of wages and employment
in unionized labor markets have been routinely exposited in the literature
for several decades. We have called one the labor demand curve
equilibrium model (LDEM) and the other the contract curve equilibrium
model (CEM). On some occasions one of these models has been
used as a framework for empirical research, and on other occasions
the second model has been used. On all these occasions, however,
each model was taken to be the maintained hypothesis. By contrast,
the primary motivation of this paper is to determine which of these
two models (if either) is the empirically relevant one in any given
labor market setting. To this end, we have set up these two models in
a manner in which the choice between them comes down to a standard
test for determining whether a particular term may be excluded
from a regression equation.
In one sense, this test is asking much more of the LDEM because it
specifies a unique solution for wage rates and employment for any
given values of the variables (a solution that satisfies eq. [4]), whereas
the CEM is compatible with a whole combination of different wage
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S34 JOURNAL OF POLITICAL ECONOMY
rates and employment depending on the particular objective functions
of the parties (as is evident from figs. 3 and 4 and the inspection
of eq. [5]). Therefore, the LDEM imposes sharper restrictions on the
parameters of our critical estimating equation than does the CEM. On
the other hand, it should be recognized that this is not simply a property
of the test that has been devised in this paper but is present in any
attempt to discriminate between the two models.
Our particular case study concerns the ITU and the operations in a
newspaper's composing room, and we find, for a wide variety of
specifications for trade union objectives, that the exclusion restriction
in our critical estimating equation is not justified, that the LDEM is
not an appropriate description of this labor market, and that the CEM
comes closer to providing a satisfactory explanation. When the fitted
relationship is interpreted in terms of the CEM, the estimated parameters
of the union's objective function provide a clear indication, rejecting
the popular view that unions maximize rents. One inference
about union objectives suggested by our estimates is that the ITU
appears on the margin to place a higher value on employment than is
implied by a pure rent-maximization objective.
Naturally, at this stage of the research, it would be imprudent to
hold to these conclusions with great confidence. There is clearly a
good deal more work that should be done on this and on other bodies
of data. Our purpose has not been to act as advocates for the CEM or
for the LDEM-surely neither of these models is the relevant one in
all labor markets at all times. Our main purposes are simply to stress
the fact that these two models imply the satisfaction of different relationships,
to present a simple procedure for discriminating between
the two models in any given context, and to encourage the application
of this procedure in other contexts.
Appendix
This Appendix presentsthe formulasused to compute the standarderrors
reportedin the text for parameterestimatesof the productionand the marginalrateof
substitution(MRS)functions.We haveavailablea paneldataset
consistingof data on J unions and newspaperswith Tjtime-seriesobservations
(not necessarilya year apart)on the jth union and newspaper.Thus
estimationiscarriedout usinga totalof n = TI1Tjobservations.Itisassumed
here thatover timethe errorsfor anyparticularunion or newspaperappearing
in the relationsfor the productionand the MRSfunctionsgivenbyequations(6)
and (10) followan mth-ordermovingaverageprocessand thatthese
errorsaredistributedindependentlyacrossthe differentunionsand newspapers.
The notation used in this Appendix is distinctfrom that used in the
body of the paper;the readeris cautionednot to confuse symbolshere with
those introducedearlier.Some detailsare presentedin the followingdiscussionto
motivatethe methodsand formulasusedtocomputetheestimatesand
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S35
the standard errors reported in the text, but rigorous proofs are absent. For
the interested reader, many of the ingredients for such proofs can be found
in White and Domowitz (1984).
ComputingStandardErrorsfor 2SLS EstimatesAccounting
for ArbitraryHeteroscedasticityand Autocorrelations
Regarding the estimation of the production function given by equation (6),
write the tth observation for the jth newspaper on this structural relation asfj,
-f(Yj,, 'y) = fit where the elements of the vector Y1,provide data on output,
inputs, and the dummy variables appearing in equation (6), and the vector y
includes parameters of the production function. Stack these observations to
form the n-component vector f '(-y) (f l, f, lT1,f
2i, f); letfi = Ei
denote the ith element of f(y); let F(,y) =af/ay'l, represent the matrix of first
partials evaluated at the parameter value y; and define X as an n X K matrix
of instrumental variables used to calculate two-stage least-squares (2SLS) estimates,
and the vector X as the ith row of X. To compute an estimate i for the
value yothat represents the "true" value of the coefficients of the production
function, the application of 2SLS calculates j' by minimizing the distance
function L(y) -f'(y)X(X'X)- 1X'f(y) with respect to y. Thus the solution to
the system of equations L-y(j) aLlayly = 0 defines A.
Taking an exact first-order Taylor expansion of this equation around the
point yo and solving for the quantity j' - yo yields the relation
(a - "o) = -L ,!(yb)L,(Yo), (A1)
where L.,,(_y) =
d2L/&aya-y'JIydenotes the matrix of second partials evaluated at
y, and 'Yb is a point between j and yo. As in a conventional application of
2SLS, the consistency and the asymptotic distribution of j' depend on the
large-sample behavior of the gradient vector L.,(y) = 2F'X(X'X) - 1X'f evaluated
at yOand, in particular, on the asymptotic properties of the quantity
X'f(yo), which is the key component of this gradient.
The quantity n 1X'f(-yo)= n - 1n=IXi-E-n- 1=uI represents an average
of random vectors each of which has zero mean. Under the conditions considered
here, one may view the observations u , U.n as being generated by an
in-dependent stochastic process, where:
DEFINITION.The sequence ul, u2,... is said to be in-dependent if the two
subsequences (. . .U, U- I, Ur)and (Us,us+ 1, . . .) are independent whenever s r>
m ? 0.
To possess this property it is not necessary that the u's have common variances
or that a stable correlation structure relate the u's to their respective
adjacent observations. In particular, if the errors for each newspaper in a
panel data setting follow generally specified moving average schemes, even
ones whose coefficients vary over time and across newspapers, and the errors
are independently distributed across newspapers, then (ul, . . ., u,,) can be
interpreted as being in-dependent. It is irrelevant for this property whether
observations are two or more periods apart or whether adjacent observations
in the sequence ul, . . ., un are associated with different newspapers (which
occurs at the beginning and the end of the subsequence corresponding to any
particular newspaper). Consequently, to obtain standard errors for 2SLS in
this panel data context, one can apply asymptotic distribution results found in
the time-series literature for in-dependent processes.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S36 JOURNAL OF POLITICAL ECONOMY
To this end, we turn to theorem 7.7.9 of Anderson (1971), which provides
the basis for the following result.
THEOREM.If u1, u2,... is an r-dependent sequence of random vectors with
zero mean and with uniformly bounded third moments and if the matrix
n m n
Vo = lim [n' > E(uiu-) + 2n'> E E(uiu'-)]
nx i=t j= 1 i=t+j
exists and is independent of t, then the normalized sample average
\/<- T,'= lui converges in distribution to N(O, VO).
In the panel setting considered here, the ui's will satisfy the conditions of this
theorem for a wide variety of circumstances, in which case we have the asymptotic
results n- 'X'f(-yo)4 0, and \?- 'X'f('yo) d N(O, Vo), with Vo being the
probability limit of the matrix V(yo), where
n m n
V(-y) n- 3XififiX' + 2n' 1 3 Xijiixt.
i= 1 t=1 i=t+1
Using these implications in conjunction with relation (Al), one can infer
the approximate large-sample distribution of the estimator sj. In particular,
assuming satisfaction of familiar regularity conditions of the sort maintained
in theorems 4.1.3, 8.1.1, and 8.1.2 of Amemiya (1985), one can prove the
following four results: (i) j' 4 'yo;(ii) \/nL- I(yb)L..(yo) - B('yo)<V 'X'fI(yo)
4 0 with the matrix
B(-y) n[F'X(X'X)- 'X'F]- 'F'X(X'X)-';
(iii) B(j') -> B(yo); and (iv) V(j') -> V(yo).
Combining these findings leads to the conclusion that in large samples
, N[yo, n- 'B(j')V(-?)B'(j')]; (A2)
that is, j' is approximately normally distributed with mean yo and variancecovariance
matrix n- 'B(j')V(j')B'(j'). The standard errors reported in the
paper for coefficients of the production function are based on (A2) with m = 3.
ComputingStandardErrorsfor 2SLS EstimatesBased on PreestimatedQuantities
Accountingfor ArbitraryHeteroscedasticityand Autocorrelations
Concerning the estimation of the MRS function given by equation (10), write
the tth observation for the jth union newspaper on this structural relation as
git = g(Zjt, 0, y) = vjt, where the vector Zjtincorporates all the measured
variables appearing in this equation, the vector 0 contains parameters of the
MRS function, and -y is the parameter vector of the production function.
Define g'(0, -y) = (g, 1, . . ., gJTj), gi as the ith element of g(H, -y),G0(0, -y)
aglao0'I0,-and G,(0, 'y) ag/a'y'I0',,.To compute an estimate for the true
value of the MRS parameters denoted by 0o, we apply nonlinear 2SLS fixing
-yequal to the estimate obtained by the 2SLS method described above. Thus
this procedure involves calculating the estimate 0 by minimizing the distance
function Q(0, j')-=g'(0, j')X(X'X)- IX'g(0, j') with respect to 0. Thus QO(0,
j')-=aQ/a0I6,, = 0 defines 0.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S37
An exact first-order Taylor expansion of this system of equations around
the points 00 and yo yields
Q0(00o'Yo)+ Q00(0s 'Sy)(6- 0o) + Q0oy(Oc,Y)(iY - 'Yo)= 0,
where Qoo(O, y)1(a2Q/dO)0.1y and Q 'y) (d2Q/aO-y')I0yare matrices
of second partials, and (0?, T) is a point between (0, jy) and (0o, yo).
Solving this equation system for 0 - 00 and using (Al), it follows that
(0 - Oo) = H(0C, Yc, lyb)h(0o, yo), (A3)
where H(O, 'Yc,Yb) =[HI H2] is a partitioned matrix with H1 = Q- 1(0,
yj) and H2 =
Qjok,, y,)Qoy(0,, Yc)L-r(7b), and h(Oo, yo) - (hi, h2)' is a
partitioned vector with hi Qo(0o, yo) and h2 L-,(yo). A comparison of
(A3) with (Al) reveals that the expressions for 0- 00 and j - 'yohave the
same basic structure. In particular, the matrix H in (A3) plays a role analogous
to L- 1in (Al) and, since h = MW with
2 [ FyX(X'X)YI
and W W(0, -y) = jwj(0, Sy)-= I (giX!,fiX')', the vector h has the same
structure as L, with M and W corresponding to the quantities F'X(X'X)'
and X'f. Consequently, one can directly apply the analysis of the previous
discussion to determine the asymptotic properties of the estimator 0.
Assuming that the error terms of the MRS and the production functions
for a given union newspaper follow a bivariate moving average process and
are independently distributed across the different union-newspaper observations,
the quantity Vn- 'W(0o, yo), like - - 'X'f(-yo) in the preceding analysis,
represents a normalized sample average of an r-dependent error process
with each observation having zero mean. Assuming the conditions alluded to
in the theorem above, it follows that V-- 'W(0o, yo) d N(O,flo), with fl0 being
the probability limit of the matrix Q(0O, yo), where
n m n
Q(0, Sy)_ n-'ZE wiw! + 2n-Z I w-w
i=1 t= 1 i=t+ 1
With this result, satisfaction of standard regularity assumptions permits
one to show the following four asymptotic results: (i) 0 4 0o; (ii) \/'nH(0c,
lYc,^Yb)h(0o,yo) - R(0o, yo)V- 'W(0o, -yo)A 0, where R(0, -y) [R1 R2]
is a partitioned matrix with
RI _R1(0, y) -n[G4X(X'X)-'X'Go]-'G4X(X'X)-',
and
R2--R2(0, 'Y)=[G4X(X'X) X'G0] [G4X(X'X) X'Gy]B;
(iii) R(0, A) 4 R(0o, yo); and (iv) fl(0, jA)4 f(0O, Yo).
Accumulating these findings implies that in large samples
6 - N[0o, n- 'R(0, J)f(0, )R'(0, jA)]. (A4)
The standard errors reported in this paper for the coefficients of the MRS
function are based on (A4) with m = 3.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
S38 JOURNAL OF POLITICAL ECONOMY
References
Amemiya, Takeshi. AdvancedEconometrics.Cambridge, Mass.: Harvard Univ.
Press, 1985.
Anderson, Theodore W. The Statistical Analysis of Time Series. New York:
Wiley, 1971.
Bowley, Arthur L. "Bilateral Monopoly." Econ.J. 38 (December 1928): 651-
59.
Brown, James N., and Ashenfelter, Orley. "Testing the Efficiency of Employment
Contracts."J.P.E., this issue.
Cartter, Allan M. Theoryof Wages and Employment.Homewood, Ill.: Irwin,
1959.
Coddington, Alan. Review of The Economicsof Bargaining by John G. Cross.
J. Econ. Literature8 (December 1970): 1211-12.
Cross, John G. TheEconomicsof Bargaining. New York: Basic, 1969.
Dertouzos, James N. "Union Objectives, Wage Determination, and the International
Typographical Union." Ph.D. dissertation, Stanford Univ., 1979.
Dertouzos, James N., and Pencavel, John H. "Wage and Employment Determination
under Trade Unionism: The International Typographical
Union."J.P.E. 89 (December 1981): 1162-81.
Dunlop, John T. WageDeterminationunder Trade Unionism.New York: Macmillan,
1944.
Edgeworth, Francis Y. MathematicalPsychics:An Essay on the Applicationof
Mathematicsto theMoral Sciences.London: Paul, 1881.
Fellner, William J. "Prices and Wages under Bilateral Monopoly." Q.J.E. 61
(August 1947): 503-32.
Friedman, Milton. "Some Comments on the Significance of Labor Unions for
Economic Policy." In TheImpactof the Union:EightEconomicTheoristsEvaluate
theLaborUnion Movement,edited by David McCord Wright. New York:
Harcourt, Brace, 1951.
Hicks, John R. The Theoryof Wages. New York: St. Martin's, 1932.
Leontief, Wassily W. "The Pure Theory of the Guaranteed Annual Wage
Contract."J.P.E. 54 (February 1946): 76-79.
Lewis, H. Gregg. Unionismand Relative Wagesin the UnitedStates:An Empirical
Inquiry.Chicago: Univ. Chicago Press, 1963.
Lipset, Seymour M.; Trow, Martin A.; and Coleman, James S. Union Democracy:TheInternalPoliticsof
theInternationalTypographicalUnion. Glencoe, Ill.:
Free Press, 1956.
Marshall, Alfred. Principlesof Economics.8th ed. London: Macmillan, 1920.
McDonald, Ian M., and Solow, Robert M. "Wage Bargaining and Employment."
A.E.R. 71 (December 1981): 896-908.
Pencavel, John H. "The Empirical Performance of a Model of Trade Union
Behavior." In TheEconomicsof TradeUnions:New Directions,edited by JeanJacques
Rosa. Boston: Kluwer-Nijhoff, 1984. (a)
"The Tradeoff between Wages and Employment in Trade Union
Objectives." Q.J.E. 99 (May 1984): 215-31. (b)
Porter, Arthur R.Job PropertyRights: A Studyof theJob Controlsof theInternational
TypographicalUnion. New York: King's Crown, 1954.
Rogers, Theresa F., and Friedman, Nathalie S. PrintersFace Automation:The
Impactof Technologyon Workand RetirementamongSkilledCraftsmen.Lexington,
Mass.: Lexington, 1980.
Rosse, James N. "Estimating Cost Function Parameters without Using Cost
Data: Illustrated Methodology." Econometrica38 (March 1970): 256-75.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions
EMPLOYMENT DETERMINATION S39
. "The Daily Newspaper Firm: A 24 Equation Reduced Form Model."
Studies in Industry Economics no. 76. Stanford, Calif.: Stanford Univ.,
Dept. Econ., January 1977.
Rucker, Frank W., and Williams, Herbert L. NewspaperOrganizationand Management.3d
ed. Ames: Iowa State Univ. Press, 1969.
White, Halbert, and Domowitz, Ian. "Nonlinear Regression with Dependent
Observations." Econometrica52 (January 1984): 143-61.
Zeuthen, Frederik. Problemsof Monopolyand EconomicWarfare.London: Routledge,
1930.
This content downloaded from 147.251.185.127 on Wed, 18 Mar 2015 10:33:11 UTC
All use subject to JSTOR Terms and Conditions