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ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
BEHAVIOR;
THE GENERAL BASIS OF ARBITRATOR
.^ND
COWENTIONAL
OF
.ANALYSIS
AN EMPIRICAL
ARBITRATION
FINAL-OFFER
Henry
S.
Farber and Max H.
Bacerman
Massachusetts Institute of Technology
October 26, 1984
#WP 1603-84
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
A^l
THE GENER.M BASIS OF ARBITRATOR BEHAVIOR:
AN EMPIRICAL .ANALYSIS OF CONVENTIONAL .AND
FIN.AL-OFFER ARBITRATION
Henry
S.
Farber and Max
H.
Baserman
Massachusetts Institute of Technology
October 26, 1984
#WP 1603-84
The General
An
Basis
o-f
Arbitrator Behavior:
Empirical Analysis of Conventional and Final-Of-fer Arbitration
Henry
S.
Farber and Max
Massachusetts Institute
H.
of
October 1984
Bazerroan
Technology
HpSTRACT
Tne Benerai
An
Basis of Arbitrator Behavior:
Empirical Anaiysis of Conventional
Henry
S.
F
arber and
and Final-Ot-fer Arbitration
Ma>;
H,
Barer man
Hassachusett 5 Institute of Technology
October 19B4
Central to unoerst andi ng the effect of arbitration schemes on the process
collective bargaining is understanding the process by which arbitrators
make decisions.
A general model of arbitrator behavior in conventional and
final-offer arbitration is developed that is based on an underlying notion of
This appropriate award is defined
an appropriate award in a particular case.
as a function of the facts of the case independently of the offers of the
In
conventional arbitration the arbitration award is argued to be a
parties.
function of both the offers of the parties and the appropriate award.
The
weight that the arbitrator puts on the appropriate award relative to the
offers 15 hypothesized to be a function of the guality of the offers as
measured by the difference between the offers.
In final-offer arbitration it
is argued that the arbitrator chooses the offer that is closest to the
appropriate award.
of
The model is implemented empirically using data gathered from practicing
arbitrators regarding their decisions in twenty-five hypothetical cases.
The
estimates of the general model strongly support the characterizations of
arbitrator behavior in the two schemes.
In addition, no substantial
differences were found in the determination of the appropriate award implicit
in conventional arbitration decisions and the determination of the appropriate
award implicit in the final-offer decisions.
It is concluded that the
appropriate award is a gener al i abl e construct that offers considerable
potential as a basis for judging the relative quality of outcomes in different
arbitration schemes.
I
.
Int''oduct
O-f
1
on
importance in the process
central
of
collective Dargaining
the
is
mechanism for settling disputes that arise wnen the parties fail to reach
agreement when negotiating
of
agreement
in
all
a
labor contract.
determines not only the terms
It
cases but also the probability of reaching agreement
without resort to the dispute settlement mechanism.
While the strike is the
dominant mode for settling disputes that arise in the course of negotiating
labor contracts,
areas,
arbitration procedures have become particularly important in
such as the public sector,
disruptive.
where
stril.:es
These procedures are characterized by
binding decision.
In
in
simply
a
a
though called by
wide range of areas.
For
litigation of civil disputes is analogous to bargaining with
arbitration as the dispute settlement mechanism.
is
third party making
a
addition, arbitration procedures,
different names, are used to settle disputes
example,
are deemed to be too
a
out-of-court settlement
An
negotiated settlement while an award by
judge or jury is
a
essentially an arbitration award."
The willingness of
the parties to make concessions in order to reach
negotiated settlement is based largely on what they expect to receive
do not
reach agreement.
regarding the outcome
in
In
the case of arbitration,
the event of
the parties'
failure to reach
a
if
a
they
expectations
negotiated settlement
depend heavily on their expectations regarding the behavior of the arbitrator.
1. Farber and Kat:
(1979) and Farber (1980) develop models of the
negotiation process under the threat of arbitration that highlight the role of
the expected arbitration award.
2. Of course, the details of the process are guite different.
For
example, in most labor arbitration schemes the offers made by the parties in
an attempt to reach settlement are admissible as evidence before the
arbitrator.
However, in civil litigation, pretrial offers to settle are not
admissible as evidence.
This difference can have profound effects on the
bargaining process.
See, for example, Wheeler (1977) and Farber (1981).
Thus,
our ability to understand tne effects
an
c-f
arbitration scheme on tne
collective baraaining process without understanding the decision processes
the arbitrators themselves is quite limited.
in
the way
In
o-f
this
systematic analysis
study two types of
first is called conventional
of
However,
there has been little
how arbitrators actually decide."
arbitration schemes are considered.
The
arbitration where arbitrators are free to impose
any settlement they see fit.
The second
is
called final-offer arbitration
where arbitrators are constrained to make an award that is equal
union final
o-f
offer or the management final
offer.
4
to either
the
While the use of
conventional arbitration arbitration has been increasing, critics have argued
that arbitrators tend to "split the difference" between the offers of the
parties resulting in
a
"chilling" of bargaining and excessive reliance on the
arbitrator to reach agreement.
This may occur as the parties maintain polar
positions in order to influence the arbitration award most favorably.
Final-
Exceptions to this are Ashenfelter and Bloom (1964), Bazerman (in
and Bazerman and Farber (in press).
A, There are many variants of final offer arbitration.
For example, where
there is more than one issue in dispute, the arbitrator may be constrained to
award the entire package of one party or the other or the arbitrator may be
free to choose final offers on an issue by issue basis.
Another variant of
final-offer arbitration, used for public employees in Iowa, gives the
arbitrator the third option of awarding the recommendation of a "neutral"
third party (Gallagher and Chaubey, 19B2).
In this study we consider only the
case where there is a single issue in dispute, and we use the simple
conception of final-offer arbitration where the arbitrator has two discrete^
options.
5. Wheeler (1978) and Kochan and Baderschneider (1978) present evidence
regarding the diffusion of conventional arbitration schemes. Feigenbaum
(1975), Feuille (1975), Northrup (1966), Stevens (196e), Starke and Notz
(1981), Bonn (1972), and Anderson and Kochan (1977) present arguments that
arbitrators split the difference in conventional arbitration resulting in a
"chilling" of bargaining.
6. Farber (1981) presents a theoretical model of arbitrator and negotiator
behavior in conventional arbitration with implications for the pure solit-thedifference model.
Bazerman and Farber iin press) present an empirical
analysis of arbitrator behavior that addresses the issue of splittina-the3.
press),
offer arbitration was developed
in
response to this criticism ot conventional
arbitration.
analysis of the relative merits
Careful
of
alternative arbitration
schemes requires comparisons in at least two dimensions.
The first
frequency with which the procedures induce the parties to reach
settlement without resort to an arbitrator.
negotiated and arbotrated settlements.
a
is
the
negotiated
The second is the quality of
both
Virtually all existing work comparing
conventional and final-offer arbitration has focused on settlement frequency,
probably because the driving force behind the adoption of final-offer
arbitration was the arguement that it is more conducive than conventional
arbitration to negotiated settlemets.
Another important reason for this
constant across different
focus is that there has been no clear standard,
forms of arbitration, that can serve as
a
basis for judging the quality of
settl ements.
It
is argued
"appropriate" award,
iadependent
of
this study that there is
in
a
construct, called the
implicit in the behavior of arbitrators that is
the particular type of arbitration and that
standard for judging the quality of settlements.
The central
that arbitrators make decisions in the different types of
based on the same underlying appropriate award.
argued to be
a
function of the facts of
p
offers of the parties.
It
is
a
a
is
a
natural
hypothesis is
arbitration schemes
The appropriate award is
given situation independent of the
representation
of
what the arbitrator would
difference directly.
7, See, for example, Kochan and Baderscheni der (1978), Neale and Barerman
(1983), and Not: and Starke (1978).
8. Throughout this study the "facts of the case" refer to all
In
considerations with the exception of the positions of the parties.
general, the facts can be considered to be exogenous to the bargaining process
while the offers of the parties clearly cannot be considered exogenous.
"unbiased" examination
award based on an
or
consideration
award is
a
schemes,
it
of
the offers.
stable and gener
al
i
:
As
ab
1
e
such,
(both negotiated
and arbitrated)
arbitration of various types.
arbitrator behavior
in
to the extent
that the appropriate
construct across different arbitration
serve an important role as
can
the facts without any tcnowledge of
o^
a
basis for evaluating outcomes
that are reached under the threat of
The plan of
conventional
this study is to devlop
and final-offer
of
an
model
of
arbitration based on the
appropriate award and to implement this model empirically
determine whether the construct
a
appropriate award,
in
in
order to
fact,
generalizes
across types of arbitration.
The ne>;t
section contains the development of
a
simple model of
arbitrator decision making in conventional arbitration where it is argued that
the arbitration award is
offers of the parties.
the quality of
are.
9
a
weighted average of the appropriate award and the
The weights are argued to be systematically related to
the offers as measured by how close to agreement the parties
Section III contains the development of
a
simple model of arbitrator
decision making in final-offer arbitration where it is argued that the
arbitrator chooses the offer that is closest to the arbitrator's notion of an
appropriate award.
The key to the empirical
analysis is the investigation
appropriate award implicit
in
the conventional
appropriate award implicit
in
the final
course, only the actual
of
how close the
arbitration award is to the
offer arbitration decision.
arbitration awards are observable.
Of
The appropriate
9. This model has as a special case the pure split-the-difference model
arbitrator behavior that serves as the basis of the critique of conventional
arbitration.
The empirical implementation of this model will shed light on
the extent to which the arbitrator sol ts-the-di f erence as opposed to
fashionino an award based on the facts of the case.
i
of
award is directly observable in neither type of arbitration so that the
investigation must be based on
a
arbitration award in each type
o-f
structural model
that relates the actual
arbitration both to the facts
o-f
the case as
they are hypothesi:ed to e-ffect the appropriate award and to the o-ffers of
parties.
The empirical
test
is
the
based on the degree of correspondence between
the observed and unobserved determinants of
the appropriate awards in the two
types of arbitration.
What are needed are data on the decisions of
arbitrators in both
conventional and final-offer settings along with the facts of the particular
case and the offers of the parties.
However, data related to arbitrators'
decisions in actual cases of the sort generally analyzed have serious
limitations for the problem at hand.
offers are recorded
Second,
in
actual
in
First,
it
is
rare that explicit last
situations where conventional arbitration is utilized.
cases do not include both conventional and final-offer awards
the same situations.
Finally, the facts available to the arbitrator are
generally incompletely observed by the investigator.
all
This is crucial because
facts available to the arbitrator, including those the investigator does
not observe,
will
affect the offers of the parties as they attempt to
These shortcomings are critical
influence the arbitration award favorably.
because the analysis relies fundamentally on identifying the role
available to the arbitrator from the role
of
of
of
the facts
the offers in the determination
the arbitration award.
In
light of these shortcomings,
the models of arbitrator behavior are
implemented empirically using data gathered from practicing arbitrators who
10. Farber (I'Jeo, 1981) develops models of strategic behavior in
conventional and final-offer arbitration where the offers are manipulated by
the parties as they attempt to maximize the value of the outcome.
were each as^ed to oecide the same set of
Both conventional
twenty-five hypothetical cases.
final-offer arbitration awards were recorded from each
and
arbitrator for each case.
arbitrators were given
a
the simulation exercise used here,
In
precisely controlled set
of
the
information regarding the
facts of each case along with information regarding the offers of the parties.
All
of
the variation
information set
of
facts of the case,
in
the facts is measured
the arbitrator
and
conventional as well
as
is
in
Thus,
the data.
the
completely characterized bv the observed
the last offers are available for use in analyring the
the final-offer arbitration awards.
each arbitrator provided both conventional
and
The fact
that
final-offer awards in all
situations is another advantage of these data because it facilitates the
estimation of the correlation between unobservable factors that affect the
determination
of
an
appropriate award by
This correlation will
case.
a
given arbitrator in
a
particular
prove to be an important part of the empirical
analysis given that the facts and the offers do not e?;plain all of the
variation
In
in
arbitration awards.
section IV the design of the simulation exercise is discussed and the
resulting sample is described.
Section
V
contains the empirical
specifications of the models of arbitrator choice along with
a
discussion of
some conceptual
issues that have implications for the econometric
specification.
An
determinants
the appropriate award
proposed.
At
of
unconstrained model that allows for completely different
in
the two types of arbitration
is
the same time it allows for correlation between unobserved
factors that affect the appropriate awards in the two types
fully constrained model
is- also
appropriate award is determined
arbitration is also proposed.
proposed where
in
it
is
arbitration.
assumed that the
exactly the same way
Finally,
of
in
both types of
two partially constrained models are
A
proposed, the estimates o^ which will
shed additioncl
lignt on how the
appropriate awards might dif-fer across arbitration schemes.
In
section VI the various models sre estimated using the data
simulated arbitrations.
It
is
in
the
found that the determinants oi the apprbpriate
awards are remarkably similar.
appropriate award
-from
All
the parameters determining the
of
arbitration are very close to the parameters
conventional
determining the appropriate award
in
nal -offer
f
arbitration.
At
the same
time the unobserved factors affecting the appropriate awards are very highly
While it is possible to reject the hypothesis that the
correlated.
appropriate awards are identical, there seems to be no substantive difference
across types of arbitration.
The final
discussion
of
the role of
1 1
,
section contains
a
brief summary of the findings as well
as
a
their implications for the evaluation of arbitration schemes and
arbitration in the collective bargaining process.
Arbitrator Behavior in Conventional Arbitration
Consider an arbitrator who must make
such as the wage change to prevail
in
a
a
decision regarding
a
single issue
collective bargaining agreement.
While it is not possible to characterize completely the objectives of the
arbitrator, one possible motivation for arbitrators is that they attempt to
make awards that maximize the probability they will
be hired
in
subsequent
cases, either by the same parties or by others who are aware of their
performance.
The process by which arbitrators are selected for cases varies
11. Where there is more tnan one issue to be decided, the details of the
analysis become more complicated but its qualitative nature is unchanged for
the purposes of this study.
acroEE settings,
but
veto power.
e;:
arbitrators
For
in
it
is
generally true tnat both parties nave
a
limited
ample, New Jersey's statuto^-y procedure for selection of
disputes involving police and firemen reauires that the New
Jersey Public Employment Relation Commission present
arbitrators to the parties, each
of
a
seven potential
list of
whom is instructed to veto three names and
indicate their preference rant:ing over the remaining four.
"
Clearly,
selection procedures such as this provide the incentive for the arbitrator to
avoid making awards are that are unacceptable to either party.
Maintaining
acceptability with both parties affects the arbitrators general professional
reputation and the freguency with which he or she will
The arbitrator who is attempting to establish
a
be hired
general
reputation will want to maintain acceptability both in terms
the parties and the facts of
the case.
Such
a
offer.
the future.
professional
of
the offers of
reputation cannot be
established by making an award that simply avoids
away from either party's final
in
a
settlement that is too far
The arbitrator's professional
reputation is also affected by the degree to which his/her settlements are
known to be consistent with the facts of the case.
this view 15 provided by Bloom and Cavanaugh
preferences
of
(1984),
Evidence consistent with
who find that the
the union and the employer regarding appropriate arbitrators in
specific cases are not in direct opposition.
that certain arbitrators are successful
at
The interpretation of this is
being perceived as fair and are
more likely to be ranked highly by both union and management in particular
cases.
A
an
behavioral
rule for the arbitrator consistent with the preceding
12. This procedure is described by Bloom and Cavanaugh (1984),
analysis of the preferences of the parties across arbitrators.
who present
argument is that the arbitrator malies an award that minimizes the sum
squared deviations
o-f
the award from each party's last of-fer
and each party's notion
union and management respectively)
award
and
(Y
eu
Y
em
awards are assumed to be determined by
(the facts)
where
a
set
nvAf s -Y em )'+(l-K)(Y s -Y eu )^]
=
V
The parameter
weights.
an
and
-for
Y
appropriate
economic and political
factors
behavior.
The
associated with this decision rule is
(V)
(l-nCMY s -Y
+
The parameters
represents the arbitration award.
Y
of
urn
These appropriate
that are not influenced directly by the parties'
loss function
(1)
o-f
union and manaoement respectively).
for
(Y
o-f
)^+(l-6)(Y -Y )^1
s
ra
K
and
5
u
are fixed
represents the weight put on deviations from the
f
parties' notions of an appropriate award relative to deviations from the
of
-f
ers.
It
seems reasonable to argue that the weight
to the offers
is
close together,
a
(H
on
function of the quality of the offers.
the facts relative
If
the offers are
the indication is that the parties are close to agreement and
the offers become of primary importance
outcomes are acceptable.
is
(y
the other hand,
On
small)
if
in
determining what
the offers are farther apart,
the penalty to the arbitrator for deviation from the offers is likely to be
smaller so that the facts become of primary importance
formal
1
()'
is
large).
More
y
(2)
q(Y
=
y
-
where g(')
is
a
Y
)
m
u
monotoni cal
The optimal
1
y
increasing function
(loss minimizing)
of
its argument.
arbitration award based on these
considerations is
Y*
(3)
=
s
where
Y
e
is
+
jTY
(l-y) (6Y
e
+
m
the weighted averaqe of
appropriate award.
This is
(1-6)
Y
)
u
the manaqement
and
union notions
of
an
10
(4)
=
Y
KY
e
This Quantity
award.
(V
)
The value
(l-K)Y
+
em
called here the arbitrator's notion
15
has normative appeal
Y
o-f
eu
to
an
o-f
the e>;tent that
aopropriate
it
suirimarires
"
e
the arbitrators interpretation and synthesis of the needs of
function of the economic and political environment.
represents the ideal
In
a
the parties as
limited sense
a
it
award.
The key result
is
award for the arbitrator to
that the optimal
weiahted averaae of the appropriate award
(Y
)
mal.e
1
5_
a_
based on the facts and the
e
offers of the parties where the weight
offers.
(H depends
on
the quality of
the
.
This characterir ation of the arbitration award is intuitively
plausible, and it need not depend on the specific parameterization of the
.
optimization process outlined here.
The optimal
arbitration award defined
interesting special cases.
and the arbitrator
First,
if
K=i
ignores the offers.
in
equation
has
(3)
a
number of
then only the facts are important
Second,
if
>'
=
and
6
=
1/2 then
the
arbitrator simply splits the difference between the offers of the parties
without regard to the facts.
is
the special
case where
that the weipht on
)'
=
Third,
but
6
a
is
more general
unconstrained.
relative to the offers is
Y
spl
a
i
t-the-di
Finally,
f
erence model
the notion
function of the quality of
e
the offers can be tested by assuming an appropriately general
for
y.
All
of
these special
presented below.
specification
cases are tested using the estimates of the
m
d
e
11
III.
Arbitrator Behavior
In
No compromise
a
Final-OHer Arbitrction
finai-of^er arbitration the arbitrator is constrained to make an
award that is equal
final
in
to the
allowed.
is
offers specifying
a
union -final
conventional
future.
by the choice of
final
of-fer.
single issue, such as the wage change to prevail
in
Assume that the underlying motivation of
"
to the motivation
offer arbitration is identical
arbitration:
to maximize
the probability of
the arbitrator must signal
However,
the management
or
Suppose that the arbitrator must choose between
collective bargaining agreement.
the arbitrator in final
o-f-fer
being hired in the
the quality of the award simply
The problem for the arbitrator is to
one offer or the other.
decide which offer is more likely to be deemed acceptable.
of
economic and political environment.
more formal
final-offer arbitration can be conceived
This requires an
the relevant facts regarding the
evaluation of the offers in the context
In
in
of
minimizes the value of some loss function.
terms,
as selecting
the arbitrator in
the offer that
However, there is no reason to
believe that the appropriate loss function in final-offer arbitration is the
same loss function that is appropriate in conventional arbitration.
The
structure of the process is quite different, and the offers play very
different roles
in
the two types of
arbitration.
Assume that the loss function of the arbitrator in final-offer
arbitration is
a
weighted sum of squared deviations of the selected offer only
from the appropriate
outcomes of the parties
^
'^
(Y
em
and
Y
)
eu
and not
from the
13. As discussed in the introduction, where there is more than one issue
dispute, final-offer arbitration can take on a number of different forms.
By assuming that a single issue is in dispute, the definition and analysis of
final-offer arbitration is simplified without losing the central features of
the process.
See Crawford (1''79) for an interesting analysis of negotiation
under the threat of arbitration where there is more than one issue in dispute.
in
the G-f-fers.
This loss -function
(5)
=
V
K(Y -V
5
)^
em
is
)".
-Y
+(1-|X) (Y
5
eu
Since the arbitrator is constrained to impose one or the other
as
the award,
award -from the arbitrator's point
the optimal
o-f
o-f
the
oHers
view is the
offer that yields the lower value for the loss function defined in equation
(5).
It
straightforward to derive the result that the management's offer
15
be selected
will
+Y
(Y
(6)
u
where
)
/2
m
<
Y
e
defined in equation
is
Y
and only if
if
(4)
as the arbitrator's notion
of
an
e
appropriate award.
This result has the intuitively appealing interpretation
that the arbitrator selects the offer that is closest to
"'
Y
.
e
In
summary, arbitration awards in both conventional
arbitration depend on the offers
a
and final-offer
common underlying variable called the
1 4
It wo uld be odd for the squared deviations of the award from the
offer s to ent er directly in the loss function in final-offer arbitration
becau se the a rbitrator must select one offer or the other.
The contribution
to th e loss f unction would always be zero from the offer selected and the
wei gh ted squa re of the difference between the offers for the offer not
sel ec ted.
In deed, if the weights are equal (i.e., 6=1/2 in equation 3) then
the c ontribut ion to the loss function from this source would be independent of
the a rbi trat i on award.
5. A mor e general characterization of arbitrator choice in final-offer
ar bi t ration i s that the arbitrator does not weight deviations from Y
by the
manag ement an d union equally.
This is equivalent to assuming that the
arbi t rator co mpares Y
While
to an arbitrary weighted average of the offers.
not p resented in this study, estimates of such a model yield virtually no
impro vement i n the fit, and the hypothesis that the weights are equal (1/2)
canno t be rej ected at any reasonable level of significance.
This is
equi v alent to the result reported by Ashenfelter and Bloom (1984).
6. If it is assumed that in final-offer arbitration the arbitrator
minim ires the same loss function that was minimized in conventional
arbi t rat i on
the optimal award in final-offer arbitration is the offer that is
cl ose St to th e optimal award in conventional arbitration defined in equation
(3).
Empi r c al implementation of this alternative formulation leads to the
concl usion th at the relationship in (6) is an adequate characterization of the
arbi t rator s decision rule in final-offer arbitration.
Indeed, for specific
val ue s of y a nd 6 (>' =
o£ 6 = 1/2) it can be shown that the alternative
f ormu 1 at 1 on
c ollapses to
the decision rule defined in (6).
1
1
,
1
'
1
13
appropriate award
average
of
(V
conventional arbitration the award is
In
).
and the of-fers where the weiahts oepend on
Y
-
e
oHers, while
closest to
IV.
Y
in
tinal-o-ffer arbitration the award
weighted
the Quality
the offer
is
a
the
o-f
that is
.
The Data:
Design
o-f
the Simulation and Characteristics of the Sample
The models developed in this study are implemented empirically using
data collected from
arbitrators.
of
set
of
simulations administered to practicing
The simulation materials were sent out
the National
regional
a
Academy of Arbitrators
to the entire membership
and the participants in
(NAA)
meeting of the American Arbitration Association
arbitrator was asked to judge twenty-five hypothetical
(AAA).
make under
conventional
a
a
Each
interest arbitration
cases where the only remaining unresolved issue was wages.
provide the wage award for
a
They were asl;ed to
contract of one year duration that they would
arbitration scheme.
the offer that they would select
in
a
They were also asked to provide
final-offer arbitration scheme.
Along
with their judgments in the twenty-five cases each arbitrator was asked to
supply information regarding his or her background and experience.
Arbitrators were required to supply their names and addresses with their
response only
if
they wished to receive
a
copy of the results.
guaranteed, and responses were sent back in
a
Anonymity was
provided business reply
envelope.
584 sets of
Of
responses.
A
total
of
materials mailed, sixty-four arbitrators provided usable
1522 usable arbitration decisions from the sixty-four
arbitrators were obtained and are used
1"^.
Thic
I'c
an
pvorppc
H'^
'^3.'^
in
(r'lt
the subsequent analysis.
Of
25 D0S?!bi8'
The mean
v?]in ^"85000=9'
14
age cf
the response group was 59 years,
were male.
1
6
The mean number ot
and
all
interest arbitration cases that had been
heard by members of the response group was 29,
arbitration cases
of
all
the respondents
two of
but
while the the mean number of
sorts that had been heard was B86.
Unfortunately,
there e!:ists no comprehensive survey of members of the NAA that could be used
to determine
arbitrators as
(personal
members
(a
the response group
if
a
whole.
communication,
is
representative
of
However, some ongoing research by Helburn and Rogers
1983),
who obtained 286 responses to
response rate in excess
of
50 percent)
average age of 60.5 years.
The mean number of
heard by their respondents was 13.1,
interest arbitration cases
Thus,
the same time,
significantly more experience in arbitration
total
arbitration
the smaller number of
respondents to the survey used in the current study had
At
survey of NAA
Their sample had an
and the mean number of
cases heard by their respondents was 295.3.
a
that required far less time
from participants, presents an interesting contrast.
age to this large sample.
the population of
a
very similar mean
the current sample possesses
of
both types.
This is
consistent with the notion that arbitrators sel f -sel ected at least in part on
the basis of
interest arbitration experience.
It
is also likely that
those
who responded were those who felt most comfortable making an award on the
basis of the information provided and who believe that the salient features of
a
real
collective bargaining situation can be captured
in
a
simulation.
It
is
difficult to speculate about the effect that these selection criter-ia might
arbitrator.
Some arbitrators responded only to some of the scenarios, and
some responses were deleted due to obvious errors on the part of the
respondents in writing their award.
18. The mean characteristics of the respondents are based on the sixty of
the sixty-four arbitrators who provided their personal characteristics along
with their judgment s.
15
have on the results.
The simulations are cast
in
the private sector
oesDite the fact that
most experience in the United States with interest arbitration is in the
One important reason
public sector.
is
that there is more room for presenting
cases to the arbitrators that are diverse in the sense that they are located
in
different settings while at the same time controlling the relevant factors
in
a
precise manner.
For example,
in
the private sector there are
a
large
variety of industries and occupations that can be incorporated into the
scenarios.
the public sector there is only one industry by definition,
In
the number of
occupations is quite limited.
and
The scenarios used here are much
more likely to be effective in manipulating the facts from the arbitrators
perspective
if
case to case.
the industrial
and
occupational
settings differ sharply from
Arbitrators may be more prone within an industry or the public
sector to make comparisons
(implicit or explicit)
between scenarios that are
unintended from the researcher's point of view and destructive of the
analysis.
we would further
Overall,
argue that the sort of decision processes
that are the focus of this analysis generalize beyond the particular sector.
The forces that
influence arbitrator behavior are likely to be similar,
much can be learned about arbitrator behavior in general
and
from examination of
the particular scenarios used here.
In
order to maintain parallelism between cases while providing necessary
diversity, twenty-five industries were identified that had varying average
national
wages in 1980.
create
systematic pattern
.40,
a
.45,
.50,
.
.
.
These national
1.55,
of
wages were adjusted very slightly to
twenty-five national wages that varied from
l.eO times $B.66,
where $6.66 was the mean of all
twenty-five actual national industry average wages.
wages were used as
a
These adjusted national
basis for the computation of some of the factors as
16
described below.
Two additional
particular values
•for
criteria were used
First,
each factor.
in
the union's -final
all
selecting the
was desired that the scenarios
it
develop wage increases rather than wage declines.
for
in
Second,
it
was necessary
offer exceed that of the management for obvious reasons,
scenarios.
Along with information on the national
wage,
each scenario contained
information on seven factors.:
-
-
The inflation rate was stated to be
-
or
127.,
11'/.,
13'/.,
or
157.,
147..
egual
to the average national
1087.,
or
wage in the industry times
B77.
,
94
7.,
1017.,
1157..
The present wage was stated to be equal
9B7;,
99.57.,
The financial
or
to the average national
wage times
102.57..
health of the firm was stated to be terrible, poor, fair,
excellent.
or
1017.,
I''
Management's final offer was stated to be equal to the average national
wage in the industry times
-
97.,
,
wage for similarly qualified employees was stated to be
The average local
good,
-
107.,
B7.,
67.,
96.57.,
-
"/.
The average wage increase of othe'' contracts in the industry was stated to
be
-
7
Uni on
'
5
final
o-f f
er
the industry times
Each of
1047.,
105.57.,
1077.,
was stated to be equal
111.57.,
1137.,
114.57.,
the twenty -five hypothetical
to
1167.,
10B.57;,
or
1107..
the average national
or
wage in
117.57:.
cases was described in
a
paragraph
19. This is the only one of the factors that is Qualitative rather than
quantitative.
The reason is that there is no clear measure o-f financial
health that could generalize across industries and would be familiar to
arbitrators.
For example, a "good" rate of profit varies considerably across
industries.
The empirical specification takes account of the ordinal nature
of this measure.
17
in
terms ot tne seven criterion -factors.
The scenarios were designed to
ensure orthogonality between factors with regard to the unaerlying ordinal
2(')
rankings.
In
the total
set
o-f
twenty -five cases there were five cases for
2
each of the five levels of each factor.^
each arbitrator
in
the same sequence,
While the cases were presented to
this sequence was chosen randomly with
This was done in order to
respect to the factors that were manipulated.
minimize the possiblity that the order
decisions.
of
The following is an example of
Situation
the cases would influence the
a
simulated case.
IB
In a town of 102,000 people, workers with similar skills and
backgrounds to the employees of this radio and broadcasting
company were paid $8.31/hr., while the national wage in this
The financial outlook for this company
industry was ?B.23/hr.
The present
is fair in light of the 117. inflation rate.
Contract
average wage for this company's union is fB.44/hr.
negotiations have reached an impasse.
Both sides, however,
have agreed to submit final offers to you, the arbitrator, and
to be bound by your decision for a period of one year.
Comparable pay increases from collective bargaining agreements
in the industry are running about 8'/. this year.
Management's
final offer is $B.56 (a 1.4X increase) and the union's final
offer is $9.55 (a 13.2'/. increase).
There is considerable variation in the responses of the arbitrators
within particular cases.
The standard deviation of the percent wage increase
awarded by the arbitrator in conventional arbitration in
a
particular case is
never below 1.1 percentage points and it is generally much larger.
maximum is approximately 2.7 percentage points.
The
The average standard
20.
This design was selected for the purposes of other research using the
same data.
See Bazerman (in press).
This design does not imply exact
orthogonality with regard to the actual levels of the factors.
Interested
readers can contact the authors for more information.
21. Of course, this does not exhaust all of the possible interactions
between factors.
There are a total of 78125 (=5
possible combinations of
the five levels of seven factors, and there are many sets of twenty-five cases
with the desired properties.
The set selected is arbitrary in this regard.
)
IE
deviation acro5= the twentv-five cases is apDro:;
points.
Similarl>'.
and
in
friatel y
1.75 percentage
there is considerable variation in the
within particular cases.
(1522/25),
i
There was an average of 61 responses per scenario
only two scenarios did all
select the same final
offer awards
-final
offer.
In
cf
only eleven of
fewer than five arbitrators select
a
the responding arbitrators
the twentv-five scenarios did
particular offer.
Thus,
arbitrators
differ substantially in their evaluation of any particular scenario in both
types of arbitration,
and these differences may be
a
major source of the
uncertainty that has been argued to drive collective bargaining where
arbitration is the dispute settlement mechanism (Farber and Kat:,
Farber,
1980,
1979;
1981).
The empirical
analysis of arbitration awards is based on the
proportional wage increase awarded by the arbitrators.
This can be
approximated by the difference between the logarithm
the wage level
and the logarithm of
the present wage.
On
of
awarded
this basis the relevant form for
the e;;planatory variables that measure wages are as log differences from the
present wage.
The only variables that do not measure wages or proportional
condition
of
the company.
Two dichotomous variables were created to measure variation
in
this dimension.
changes are the variables measuring the financial
The first
(CONDB)
equals one
if
the financial
condition
terrible or poor, and it equals cero otherwise.
if
the financial
condition
of
The second
The omitted category is
The definitions,
means,
a
firm financial
and standard deviations of
empirical analysis are contained in Table
of
equals one
(CONDG)
the firm was good or e>;cellent,
zero otherwise.
Preliminary examination
the firm was
of
and
equals
it
condition
of
the variables used
fair.
in
the
1.
the arbitrator's responses uncovered an
interesting phenomena that is not apparent from the information
in
table
1
and
19
that fundamentally
aHects
the
emDincal analysis.
arbitration awards that were analyred.
fully 38"
either the union's or the management
last
s
Of
the 1522 conventional
(25.6/.)
All
offer.
were exactly equal
but
8
of
to
the 64
arbitrators had at least one award that was equal to one
of
the offers.
reasonable explanation for this is based on the property
of
the scenarios that
plausibility of
they were designed arbitrarily without regard for the
offers VIS
a
vis the facts.'"
skewed relative to the facts
In
A
the
those situations where the offers were
(both very low or both very high),
the
the
arbitrators often seemed to feel constrained not to stray outsiae
boundaries set by the offers though they were free to do so."^
the arbitrators did not
feel
so constrained.
In
196 cases
arbitrators) the award lay outside the boundaries.
detail,
the pattern of
(for
In
some cases
31
While not analyzed in
awards within arbitrators suggests that some
These
arbitrators are very reluctant to make an award outside the boundary.
arbitrators had
a
relatively large number
of
cases on the boundary.
Other
arbitrators felt relatively free to make awards outside the boundaries, and
they had few cases on the boundaries.
Only two arbitrators were never on
a
boundary or outside the boundaries.
With regard to the analysis of
arbitrator decision making, the issue
of
of the
why some arbitrators are more likely to make awards outside the range
offers is
a
complicating factor that will not be addressed in any detail here.
Indeed, such extreme cases are likely to occur only rarely if at all
in
actual
actual data were used it is unlikely that offers that were so
They only occur here
"pathological" relative to the facts would be observed.
This
because of the independent variation of the facts and the offers.
independent variation is an important strength of the data used here.
23. In terms of the loss function, this suggests that there ere
discontinuities at the boundaries that make it more costly to venture outside
22.
in
If
some situations.
The approach taken
practice.
to develop
is
appropriate econometric
an
specification that accounts for when arbitrators in conventional arbitration
will
be either
on
boundary
a
outside the boundary without speci-fying which
This approach, discussed in detail
these conditions hold.
of
o_[^
in
the next
allows us to proceed with the analysis of the decision processes of
section,
arbitrators where there
is
a
"normal" configuration
the facts and offers
of
without confounding the analysis with the boundary problem.
Specification
The Empirical
V.
In
sections
order to implement the models of arbitrator choice outlined in
and
II
III,
a
specification
appropriate settlement in each form
appropriate
awards
^'^
Denote the
arbitration is required.
of
an
Y
ec
and
Y
ef,
These must be based only on the facts of the case and not on
respectively.
the offers of
(7)
the arbitrator's notion of
conventional and final-offer arbitration by
in
"^
of
Convenient specifications are
the parties.
=
Y
XP
ec
+
c
e
c
and
(8)
where
Y
,
ft
Ip^
=
er
represents
X
£,
vector of variables reflecting the facts,
a
represents vectors
+
of
parameters,
and
and £,
£
representing unmeasured factors affecting
-^
>•
vector
2)
X
includes
-
a
V
ec
in
and
Y
comparable situations:
respectively.
,
ef
1)
3)
the rate of
5)
the logarithm of
f»,
The
inflation;
the differential
between the local wage for comparable work and the present wage;
differential between the national
and
are stochastic components
constant and variables measuring
negotiated settlements
P
4)
the
wage in the industry and the present wage;
the present wage;
and
6)
the financial
condition
of
the
company.
The criterion function
arbitration, contained
eauati on
(
6
)
(9)
for
Y
+Y
(Y
)/2
(Y
<
f
+Y
is
)
/2
final-o-ffer
after substituting from
£,.
f
-
Xfv
if
,
f
the analysis of
,
Assuming
selected otherwise.
is
a
normal
distribution
offer arbitration awards is
final
unlike the usual probit analysis, the variance
Note that,
simple probit.
£,
£
-
Xf'
selected
is
urn
and the union's offer
with zero mean for
be written
can
(6),
f
The manaoement's offer
£,
-
m
u
(10)
equation
in
in
as
,
et
=
II
choosing the (Tianagement o^ter
for
a
of
identified due to the fact that the average offer enters the criterion
function with
known coefficient
a
The empirical
(=1).
analysis of conventional arbitration awards is more
complicated due to the boundary problem.
general model
that relates
Assuming an additive error, the
and the offers to the optimal
Y
conventional
e
arbitration award, contained in equation
Y* =
(11)
n'
s
where
is
Y
ec
(1-n [fY
+
ec
the value of
(1-6)Y
m
+
]
«.
u
conventional
in
Y
+
can be rewritten as
(3),
arbitration and
e
component representing unmeasured factors affecting
from equation
(7)
for
Y
y*
=
s
where
and
fi
A
final
(l-n[^Y
+
+
(1-6)Y
m
refer to the values of
£
c
UP c
a
stochastic
«
Y
.
+
M
After substitution
this relationship is
,
ec
(12)
is
M
+
]
>£
u
P
and
c
£
for
conventional
arbitration,
c
quantity that needs to be specified for the analysis
arbitration awards is the weighting function that determines
of
)l
.
conventional
This is
specified as the simple linear function
(1 3
)
r
=
r.
U
where
)'
and
H
+
r
1
[
-
Y
u
Y
]
m
are parameters to be estimated.
The notion that the relative
weight on the facts
this specification as
Specification
of
ec
>.
positive value for
a
the optimal
of
the offers
and
Y
larger when the ofters are farther apart is embodied in
iz
is
not
arbitration award as
continuous function
a
consistent with the bunchinq
arbitration
of
award; at the boundaries under standard assumptions regarding the
distributions
the random components
of
the specification of
the optimal
(£
and
It
,u).
arbitration award defined
valid only for awards that lie between the offers.
or
outside the ranae defined by the offers,
when an award will
different
be on the boundary or
(unspecified)
Where
eauation
in
on
is
Y
ec
a
is
(11)
boundary
'
different process determining
a
Y
specification that accounts for
What is required is an empirical
may prevail.
also seems clear that
outside and, hence, determined by
a
process.
An appropriate statistical
is based
on
the notion that the process
is censored
in
that the process is only
model
that determines
Y
in
observed
is
interior to the offers.'^
equation
(11)
''4
if
Y
ec
process
of
arbitrators can be thought of as
arbitrator formulates
this to the offers.
a
If
equation
an award on
on
a
(11).
If
'
the decision
sequential process.
a
The
notion of an appropriate settlement
(Y
the offers surround
then the
<Y
(Y
Y
ec
arbitrator mal-es an award that is the function
in
this context,
In
ro
of
the offers do not surround
Y
ec
Y
ec
ec
<Y
)
)
ec
and compares
u
and the offers defined
then the arbitrator makes
some basis that is not articulated here except that it is either
boundary or outside the boundaries defined by the offers.
This
alternative decision process does not have to be tne same for all arbitrators
24. This is only one of a number of potential censoring processes that
could be used.
Other specifications were tried, and the results were
qualitatively similar.
The approach presented here provided tne Dest fit to
the data.
or
little structure
Tne key is tnat
cases.
all
these observations.
imposed on tne data
is
arbitration award
The data on the actual
or
used for
is
(Y^.i
i
these observations only to the e;;tent that they have information about the
relationship between
ec
the offers.
the quantity
More formally,
the offers,
and
Y
and in this case
Y
is
Y
observed only
if
Y
ec
'
'
s
is
equal
to the
interior to
is
arbitrationaward
actual
(Y
On
the other hand,
if
is
Y
ec
less than or equal
arbitration award is less than or equal to
than or equal
then the actual
to Y
).
S
5
Y
to
then the actual
Y
m
Similarly,
.
if
m
Y
GC
is qreater
"
arbitration award is qreater than or equal
u
to
Y
Essentially, the unobserved value of
.
used in determininq
is
Y
ec
u
whether an arbitration award corresponding to the process defined above is
observed.
Thus,
Y
relative to the
is
censored based on the value of
is
to derive the probabilities associated
Y
5
'
ec
offers.
The next step
Y
of
or
equal
a
The probability of observing an award that
given value.
to the management
(14)
Pr(Y
with observing
<
Y
5
=
)
is
less than
offer is
Pr(Y
m
<
Y
ec
)
Pr(t
=
<
-X^
Y
m
c
in
).
c
Similarly, the probability of observing an award that is greater than or equal
to the uni on
(15)
of
f
er
Pr(Y
>
s
Finally,
i
5
Y
=
)
u
Pr(Y
>
ec
Y
)
Pr(£
=
u
a
value equal
to
>
Y
-Xp
).
observing an award that is between
the joint probability density of
the offers and that has
cue
Y
is
Pr(Y <Y <Y
(16)
(T'SU
other words,
Y
,
ec
and hence
Y
=Y*)
5S
Pr(Y
i
£
or
,
all
<;Y
-XB
falls.
However,
-;Y
is
it
Y
yS
Y
.
=Y -(Hf'
cs
c
known
what range the value of
in
and hence
,
=V*)
£5
m
W-t-yS
,
]}).
u
observed only
is
if
c
s
The key to the test of
the model
arbitrator behavior is an analysis
of
how close the arbitrator's notions of an appropriate award
are in the two types of
arbitration.
trivariate normal.
Although
and
Y
ec
Y
(£
£
,
can be tested directly.
=p
unobserved components affecting
However,
it
is
and
Y
ec
not possible to apply
a
ec
Y
,)
ef
are distributed as
are not observed directly,
,
ef
In
and H)
,
More formally,
relationship with the facts can be estimated.
f>
and
(Y
assumed throughout this analysis
is
It
that the random components of the model
that
-t-d-flY
*{l-)')U,\-
between the offers.
is
EC
<Y
(TieCU
W+
,
observations
c
Y
of
=
mccuc
Pr(Y -XP <c
=
In
.
a
their
the hypothesis
addition, the correlation between the
Y
,
ef
and
(£
£ ,)
c
can be estimated.
f
standard test for the equality of these
random variables because equality implies equal variances along with unit
correlation, and the latter is on the boundary of the parameter space.
In
a
order to examine the congruence
between
^
joint model
of
arbitrator choice are estimated.
unconstrained model allows
?
c
and
Y
ec
Y
,,
ef
four versions of
The most general
and f, to have distinct values while allowing
f
for correlation between the three unobservabl es in the model
(£
,
c
The likelihood function for this model
of
is derived
£,,
and
,H).
f
from the joint probabilities
four distinct events under the assumption of trivariate normality of the
errors.
25
Letting
Y
,
sf
represent the arbitration award in final offer
25. Note that there are a total of six conceptually possible events.
However, two of these events are clearly oathalogical in some way, and these
probabilities are not specified here.
One is tne case where the conventional
arbitration and
arbitration award, tne first
represent the conventional
V
ie
5
the joint
probability that the conventional award is less than
management final
•final
the final-o-ffer award is equal
and
smstm
Pr(Y <Y
,
=Y
Y
=
)
the union final
Ne;;t,
to
the
to the management
cmctum
Pr(£ <Y -Xp
The joint probability that the conventional
(IB)
equal
This probability is
offer.
(17)
o-ffer
or
offer and the final
susfu
Pr(Y >Y
,
=Y
Y
=
)
,
e,<[Y +Y ]/2-Xf'
award is greater than or equal
offer award is equal
,
*
to
and
Y
to
offer is
e,>CY +Y 1/2-tP,).
the joint probability that the conventional
offers and is equal
to the union
cucfum
Pr(e >Y -Xp
).
t
f
award lies between the
the final-offer award is equal
to
the manaaement
offer is
(19)
Pr(Y <Y <Y
m
=
=Y
Y
,
u
s
,
mccuc
Pr(y -Xp <e <Y -XP
=Y
V
5
s
sf
)
m
cs -iUP
-Kl-riE^Y +(1-6)Y ]},
}i*H =Y
,
c
m
u
e.<[y +Y ]/2-Xp J.
u
f
ffl
f
Finally, the joint probability that the conventional
offers and is equal to
award lies between the
and the final-offer award is equal
Y
to the union
s
offer is
award is less than or equal to the management offer while the final-offer
award is equal to the union offer.
The second is where the conventional award
is greater than or equal to the union offer while the final-offer award is
equal to the management offer.
There were eight such cases in the original
sample, and it was decided that they were most likelv the result of response
error.
These observations were deleted from the sample used for estimation.
^0
fDSUSS
Pr(Y <V <Y
(20)
=Y
Y
,
.
Y
mCCUC
Pr(Y -XP <e <Y
-Xf'
.=V
s+u
,
)
CE -CHP
H-^H =Y
+(l-r)[M' +(1-6)Y ]},
C
u
IT,
e.>[Y +Y ]/2-Xp,)
In
the ne>;t
section,
are presented.
model
elements
of
include
These parameters
r
(constrained #1)
P
=P,
P
the parameters
o-f
f,,
,
c
1'^,
)",,
o-f
and
£,
this
the six'
1
-f
the covariance matri>; of the errors.
The second version
that
likelihood estimates
ms>;imum
where
and that
=Y
Y
ec
=E
€
to be estimated
the model
o-f
,
in
respects.
all
and ^, by
£
assumed
is
to the management
£.
It
o-f
is
P
and
p
by P,
straightforward to
that the conventional
award is
offer and the final-offer award is equal
offer is
<Y
Pr (Y
The probability of
,
Y
sf
m
s
=Y
)
=
Pr (e<Y -Xp).
m
m
the second event,
to the union
than or equal
it
f
show that the probability of the first event,
(21)
constrained model
Essentially,
Denote the constrained value
.
c
to the management
a
ef
and denote the constrained value of
less than or equal
is
that the conventional
award is greater
offer and the final-offer award is equal
to the
union offer is
(22)
>Y
Pr (Y
s
Next,
,
,=Y
Y
u
sT
)
u
=
Pr (£>Y
-Xp)
.
m
the joint probability that the conventional
award lies between the
It
offers and is equal to
offer is
Y
and the final-offer award is equal
to the management
27
Pr(Y
(23)
=
<Y
-::Y
m
5
,
=y
Y
u
s
o-f-fers
5t
urns
equal
is
to
)J
+
K=Y
- {i'Xf'-^
and the -final-o-ffer award
Y
(
1
-
1
)
+(l-^,)Y
[fY
m
the conventional
the joint probability that
and
)
m
Pr(Y -XP<evCY +Y ]/2-X^,
m
Finally,
.=Y
Y
,
5
]})
u
award lies between the
equal
is
to
tne union
s
D-f
-f
er
15
Pr(Y <Y <Y
(24)
m
PrCY
this model
estimates
elements
=Y
Y
,
sf
E
s
]/2-Xp<e<Y
:
u
M+
-Xf',
)'e
-
=Y
u
{nf>+
(1
-^
)
C 6
Y
m
5
+(1-MY
u
]:),
the likelihood function
can be derived from these probabilities.
The maximum likelihood
o-f
joint normality
O'f
the parameters of this model
of
of
+Y
urn
=Y
Y
the errors,
Given the assumption
of
,
u
s
the covariance matrix
of
(P,
and H)
£
T.
H
,
,
6,
and the three
are presented in the next
secti on.
The third specification of the model
(constrained *2)
no correlation
is
of
the general
is
a
constrained version
model, defined in equations
allowed between
and either
£
are allowed to differ.
or
£
'f
a
In
of
the models based on the marginal
underlying random variables.
parameters of this model
(P
other words,
P
f
(14)
-
(16).
distributions
of
The maximum likelihood estimates of
,
P.,
y
.
,
H
,
i,
these
arbitrator choice in
arbitrator decision making
of
conventional arbitration that is defined in equations
as
and
f
c
simple probit model
offer arbitration and the model
of
However,
a.
where
This is equivalent to estimating the models of
estimates can be derived from
be thought
(20),
c
conventional and final-offer arbitration separately.
final
-
(17)
in
These can
the
the
and the four free components of
the cDvanance
inetri);
specification
The final
(constrained #3)
P
but where
=f'
c
the errors)
o-f
the general
o-f
is
£
o-f
are presented in the next section.
the model
model,
is
constrained version
defined in equations
allowed to differ from
c
f
a
£,
(17)
-
where
(20),
thouah correlation is allowed
f
.g
This can be interpreted as assuming that the systematic determinants of
for.
and
Y
ec
Y
,
ef
are identical
while the random components may differ.
alternative interpretation is that
Y
ec
=Y
,
ef
in
all
An
respects while there is an
additional error component in the final-offer decision rule that causes
deviation from
a
strict comparison between the averaoe offer and
maximum likelihood estimates
and the six components of
in
the next
of
the parameters of
the covariance matrix of
this model
(P,
the errors)
Y
The
,.
ef
T.,
a
y,
6,
are presented
section.
Note that the sample design seems to be
error components model
of
a
natural
for application of
an
There are multiple observations for each
some sort.
arbitrator, and it is known that the arbitrators differ systematically in
their awards
(Bazerman,
press).
in
If
these systematic differences are not
accounted for, the inferences based on the estimates will
to the correlation
for
a
that is induced between the stochastic terms across cases
particular arbitrator.
One approach to accounting for this correlation
in
the likelihood function
in
their mean values of an appropriate award
final-offer arbitration.
on
e.'"
not be reliable due
is
to assume that
arbitrators differ systematically
(Y
)
in
both conventional
and
This is equivalent to an error components structure
This structure can be accommodated by includino
a
vector of
26. In the conventional arbitration model there is more than one error (£
and M) so that assuming systematic differences across arbitrators in Y
is not
the only possible solution.
For example, another approach would be to assume
that the mean value of
varies systematically across arbitrators (an errors
components structure on n)
Yet a third approach would be to allow the
Si
.
arbitrator speciHc dummy variables
in
the data vectors determining
Y
ec
and
ef
15
It
not
likely that the introduction of -fixed effects will
This is because each arbitrator
estimates or the inferences substantially.
was given the same set of
(X,
Y
,
m
Y
)
change the
twenty-five cases so that the explanatory variables
are the same for all
arbitrators
in
each case."
In
this
u
situation it can be shown for ordinary least squares
(OLS)
estimates derived without fixed effects are identical
fixed effects are included.
In
addition,
it
models that the
to those obtained
can be shown
that
when
the standard
errors derived from models including fixed effects must be smaller than those
''9
derived from models without fixed effects.^
Thus,
any hypothesis testing
done on the basis of OLS estimates without fixed effects will
be conservative.
While these results are not precisely true for the nonlinear model
here,
proposed
they are likely to be approximately true.
The results reported in the next section are for specifications which do
not include fixed arbitrator effects.
unconstrained model,
al
of
With the exception of
the fully
the models have been estimated including fixed
decision processes of arbitrators to differ more generally.
Bazerman (in
press) presents an analysis of the formulation of awards under conventional
arbitration that accounts for differences between arbitrators in a number of
di mensions.
27. There are 25 observations for most arbitrators so that the standard
problem of inconsistency in nonlinear fixed effect models due to small numbers
of repeat observations is not likely to be a serious problem.
A random
effects specification was considered.
However, evaluations of very high order
normal CDFs would be required, ano the computational burden was deemed
excessi ve.
28. This is not precisely true due to the fact that tnere are some missing
observati ons.
29. The analysis of errors components models in this context is formally
identical to the well known seemi ngl y-unr el ated-regressi on problem.
Note that
these considerations are independent of whether, in fact, the fixed effects
differ significantly across arbitrators.
effects."'
While tne hypotheEis that the fi>;ed effects are equal could be
rejected in all
cases,
the parameters of
the estimates or
asymptotic standard errors were virtually identical
without -fwied effects.
In
to
interest and their
the estimates derived
addition the qualitative nature
of
the outcomes of
the competing models were not affected by the inclusion of
the tests of
the
fixed effects.
VI
,
The Empirical
Results
The first two columns of
estimates
of
conventional
table
2
contain the maximum likelihood
the unconstrained joint model
of
and final-offer arbitration.
The definitions of
variables are contained
in
table
1.
All
of
arbitrator decision making in
the relevant
the estimates presented
in
this
section were derived using the optimization algorithm described by Berndt,
Hall,
Hall,
and Hausman
the sense that
all
of
The estimates of the model
(1974).
the parameters have the expected sign and are
asymptotically significantly different from zero
general
framework of the conventional
by the data.'
The weiqht on
Y
ec
at
sensitive to the quality
of
conventional
levels.
The
arbitration award process is supported
relative to the offers
the arbitrator pays primary attention to the facts,
Estimation
are plausible in
but
(P
is
larqe so that
the weight
i_5_
the offers in the sense that as the offers get
fixed effects in the fully general model would require
additional 126 parameters in a single model.
The
computational burden proved to be excessive.
Constrained model *t2 also
required the estimation of 126 extra parameters, but the estimation could be
split into two pieces.
31. Bazermen and Farber (in press) discuss a similar set of estimates in
detail with regard to their implications for arbitrator behavior in
conventional arbitration.
30.
the estimation of
of
an
31
fartner apart the weicht on
increases
Y
ec
The weight on the
(t',>0).
1
management offer relative to the union offer is significantly larger than
The estimates of
and
f'
P
c
,
are very similar so that their qualitative
t
properties can be discussed without malting any distinction.
The differential
between wages negotiated by workers in comparable situations and the present
wage
in
has
(COMP)
the local
a
large positive effect on
(occupati onal
1
y
defined)
labor markets and the present wage
than that of NW.
small
It
is
:ero at conventional
the implication
is
Y
levels.
it
is
have positive but
The effect of
.
LW
is
larger
e
interesting that the level
positive coefficient, although
(industrially defined)
and NW respectively)
smaller statistically siamficant effects on
between wages
The differential
.
national
and
(LW
Y
of
the present wage has
a
significantly different from
not
To the extent that
this coefficient
i
s
posi ti ve
that arbitrators act not only to ratify the existing
proportional wage structure but also to widen the existing differentials
somewhat.
Finally, the financial condition of the company has an asymmetric
effect on the arbitration award.
The omitted category for the dummy variables
are situations where the company is in
is
in
worse condition
1/2 percentage points
(CONDB),
"middling" condition.
If
the company
the arbitrators made awards which were
lower on average.
On
the other hand,
if
2
to 2-
the company
were in better condition, the arbitrators made awards which were about 1/2 of
32. While there is no clear interpretation of this result, it may suggest
depends
that a richer weighting scheme is needed where not only H but also
For example, it may be the case that 6 depends
on the Quality of the offers.
from Y
Some alternatives were
on the relative distances of Y
and Y
investigated, but the empirical implications of these variations are so
similar to the model estimated here that it was difficult to distinguish
between the different specifications with any precision.
See Bazerman and
Farber (in press).
(,
.
percentage pcint higher on average.
a
CONDG is
equal
o-f
be rejected
at
table
=Y
Y
ec
3
,
in
all
summarized
Y
ec
Y
4.
The first
are.
,
ef
constrained model
of
ci
ents on
It
of
the loQ"
a
classical
likelihood-
against the unconstrained model due to the
#1
fact that one of the constraints is that
P
=1
cf
which is on the boundary of the
some feel can be gained for how well
Nonetheless,
of
the constrained models are
not possible to perform
is
column
where it is assumed that
#1
"
ratio test of constrained model
parameter space.
and
the unconstrained and all
of
table
in
i
significance,""
of
The specific constraints along with
respects.
likelihood values
level
issue is how close
contains estimates
ef
-f
magnitude but opposite sign to the coefficient on CON DP can
any reasonable
The central
The hypothesis that the coe-f
the
constrained model performs by noting that the log-likelihood value for this
model
is
1536.6 as compared with 1617.3 in the unconstrained model.
implication is that
Y
ec
and
Y
,
ef
34
The
differ in ways that deqrade the fit of the
constrained model substantially.
It
is
is
useful
that P, and
f
to examine exactly how
differ substantially.
P
Y
ec
and
Y
,
ef
differ.
One possibility
The last column of table
2
contains
c
the estimated differences between
and P,
P
c
computed from the estimates of the
f
unconstrained model along with their asymptotic standard errors.
All
of
these
differences &rB small when compared to the magnitude of the coefficients
themselves.
Only the coefficients of CONDB differ significantly at
conventional
levels,
and only one other difference
(CONDG)
exceeds its
33. This hypothesis is equivalent to the hypothesis the the two
coefficients sum to :ero.
Using the coefficients from conventional
arbitration this sum is -.0124 with an asymptotic standard error of .0033B.
similar result is derived using the coefficients from P..
34. Were the lil:elihood-ratio test valid, the hypothesis that Y^^=Y_
ef
ec
could be rejected at any reasonable level of si qni f cance
.
These results suaqest that indiviaual
standard error.
elements ct
and
^'
f'
c
differ significantly Dased on their marginal
do not
it
p
IS
=P
,
distributions.
-f
However,
also important to examine the extent to which the joint hypothesis that
Constrained model #3, whose estimates are
supported by the data.
IS
contained
columns of table
the last
in
only in imposina
=P
P
,
A
.
differs from the unconstrained model
3,
likelihood-ratio test
of
the hypothesis that
=P,
P
c
t
c
f
suggests that the hypothesis can be rejected at the .05 level of significance
but not
the .025 level
at
""'
.
Another diagnostic calculation for e>;amining the degree
between P, and
the difference between
to compute
is
P
each scenario based on the estimates of P, and
A
Table
model.
Y
ef
c
f
5
contains the estimates of
conventional
Y
ec
,
ef
levels.^
and
and
Y
ec
si qni
,
ef
,
Y
ec
and their difference for
For
only four scenarios is the
cant
f
1
y
different from :ero at
"
Overall,
the evidence suaaests that
and P,
P
unobserved factors.
and
Y
ec
The variance
Y
,
ef
could differ is with regard
to the
'
differs from the variance of £, by
£
c
f
.000103 with an asymptotic standard error of
that the variances are equal
a
.0000434 so that the hypothesis
can be rejected at conventional
very hiqh correlation is estimated between
of
/'
is
.818 with
a
very small
levels.
and £..
£
c
estimate
differ
f
inconsequential extent.
The other way in which
same time
for
c
from the unconstrained
P
c
to a minor
=XB
A
A
Y
and
f
A
Y
The results are quite clear.
difference between
,
congruence
The asymptotic standard errors are also
each of the twenty-five scenarios.
presented.
=XP
of
At
the
The
t
asymptotic standard error.
The
35. The test^statistic is -2 1 61 7. 3-1 608. 6) =17. 4
This statistic is
distributed as X'^ with 8 degrees of freedom.
The critical values of this
distribution at the .05 and .025 levels are 15.5 and 17.5 respectively,
36. Careful examination of these four cases (4,18,19,21) did not reveal
any pattern that could be viewed as a common cause of the difference.
(
.
34
hypothesis that
SI
am
-f
1
cance.
egusls zero can be rejected at any reasonaoie
P
Thus,
affect
the unobserved factors that
correlated with the unobserved factors that affect
important this correlation is,
Y
ec
order to see how
In
et
constrained model
a
ere hiohly
Y
..
(#2)
of
les'el
was estimated where
P
c
and
&re allowed to differ but where
f'
p
f
These &rB the estimates of the separate
and
,
The log-lil;elihood of
3,
the unconstrained model,
is
in
this model,
Thus,
1445.7.
rejected at any reasonable level.
are assumed to equal
,
Indeed,
of
conventional and
and
third columns of
models
the second
which has only two constraints on
the constraints are soundly
this model
with two constraints
fits the data considerably more poorly than either constrained model
eleven constraints or constrained model #3 with
8
constraints.
but
with
#1
course,
Of
various constrained models, whose performances &rs summarized in table
not nested appropriately,
zero.
wf
(marginal)
final-offer choice, and they are contained
table
P
cf
the
are
4,
this comparison does suggest that the
correlations between the unobserved factors are substantial.
While there is important correlation between
€
c
IS
not perfect.
It
is
this correlation
and £r<
f
not possible to test the hypothesis that
because of the boundary problem noted earlier, but we can pick
For example,
somewhat less than one and test that hypothesis.
that
P
=,95 can be rejected against the alternative that
,
,'',
a
directly
=1
P
value
the hypothesis
<.95 at any
f c
f c
reasonable level of significance.
nested in constrained model #3.
Note further that constrained model
Model
#1
embodies the assumption that
is
#1
=£,1
£
c
,
but
of
in
all
model
#1
other respects is identical
is
1536.6 while the
1
og-1
i
to model
kel hood
#3.
it
is
log-likelihood value
value of model #3 is 160B.6.
This comparison suggests that the errors are not,
Overall,
The
in
fact,
identical.
clear that the unobserved factors affectina
are correlated to an important extent.
In
f
Y
ec
and
Y
,
ef
addition, the observed Determinants
0-f
and
Y
ec
Y
,
ef
nave similar effects.
the model
Tne ability of
tne
to fit
data 15 improved substantially bv accounting for the correlation between the
errors,
constraint
(#3)
that
=£-,.
^-
c
VII.
degrade very much bv imposing the
end the performance does not
Implications
of
f
the Analysis
The results presented in the previous section imply that there is
a
substantial amount of consistency between the decision models of arbitrators
i'n
conventional
and final
offer arbitration.
conventional
In
arbitration it
was argued that arbitrators mal:e awards that are weighted averages of
notion of what is appropriate based on the facts
parties where the weights depend on the quality
(Y
)
ec
and the offers of
the offers.
of
some
This behavior
loss function that
is
consistent with the arbitrator attempting to minimize
is
the weighted sum of squared deviations of the award from each party's
notion of an appropriate award and from the offers.
arbitration
it
In
a
the
final-offer
was argued that the arbitrators choose the offer that is
closest to some notion of an appropriate award based on the facts
(Y
behavior is consistent with the arbitrator attempting to minimize
a
function that is the sum of squared deviations
of
.).
et
This
loss
the award from each party's
notion of an appropriate award.
The results strongly support this framewort-.
arbitration awards do seem to be
The conventional
weighted average of the facts and the
a
offers where the weights are dependent on the quality of the offers.
addition, the facts all
The final
influence
In
in
a
plausible and significant fashion.
offer awards &r^ determined by
a
comparison of the facts with the
average offer,
and the value of
Y
Y
ec
,
ef
that
is
implicit in this process is
36
determined
plausible and significant ways by the facts.
in
the quantities
(?
=P
c
,)
and
Y
ec
V
,
ef
are
and the unobserved
,
affected virtually identically by tne facts
factors affecting
Y
"
f
exactly the same notion
and
Y
,
ef
are highly
"
of
appropriate award
an
in
malung decisions
both
in
the evidence is quite compelling that the arbitrators
arbitration,
of
ec
While it is not possible to conclude that the arbitrator uses
correlated.
types
More importantly,
are generally consistent
in
their behavior.
This consistency in arbitrator's views of an
"appropriate" award has
a
number of implications for understanding arbitration and collective
First,
bargaining.
these results provide convincing evidence that arbitrators
determine an appropriate award without reference to the particular form of
arbitration
in
effect.
The results further indicate that the appropriate
independent both
award can be defined based on the facts of the case,
political
and of
and structural
the final
influences
a
of
quality.
Next,
the validity of this model
That is,
of
arbitration against an independent
the agreements reached under tne threat of
conventional versus final-offer arbitration
(whether negotiated or arbitrated)
can be compared to the appropriate award as defined by the facts of
While critics of conventional
of
sound basis for comparing the quality of
agreements under alternative forms
definition
the
the particular arbitration procedure
of
offers of the parties.
arbitrator behavior suggests
of
the case.
arbitration argue that it chills bargaining,
critics of final-offer arbitration argue that it often results in unacceptable
arbitration awards.
basis
of
The model
(the appropriate award)
developed and tested
for
in
this study provides
a
judging the appropriateness of the outcomes
the two systems.
A
potential
reservation relates to how gener al
given that they are based on awards in hypothetical
i
abl e
cases.
these results are
Of
course,
having
37
arbitrators
actual
ffal-.
the awards
ing
favor of broader applicability.
is
addition, the general
In
data from simulations are important.
preciselvi
and
arbitration.
important factor militating in
an
in
using
cases of conventional
from the fact
the simulations suffer
the other hand,
of
The facts are controlled and measured
the offers are observed even
On
advantages
that the
situations are artificial by definition and that the arbitrator does not have
the same range of
5um,
it
is
information available that is available
impossible to oe sure that the judgments
of
of
actual
arbitrators
simulated cases are consistent with those they would make
Nonetheless, the internal consistency
in
tne responses of
in
cases.
In
in
actual
cases.
the arbirrators
across types of arbitration demonstrated in the analysis contained in this
study suggests that there is
great deal
a
information in these simulations
of
that can make an important contribution to understanding the behavior of
arbitrators.
Another potential reservation is related to the fact that arbitrators
final-offer judgement
were asked to render
a
conventional award.
This may imply that the final-offer awards are
i
"contaminated" and the analysis will be biased
similarities between
advantages
If
in
or
a
of
Y
and
,
ef
Y
.
ec
mmedi atel
in
v
after making
favor of finding
While this raioht be worrisome,
this approacn must be weighed against the potential
each case an arbitrator was only required to make either
final-offer award
(but
not
both)
as
P
unobservabl es affectinc
and ^^t
in
y
a
the
problems.
conventional
specified by the investigator,
limited version of the analysis here would be possible.
possible to compare
a
but no estimates of
conventional
It
would still
t
)
would be possible.
observation
of
be
and final-offer
arbitration
(£
c
Identification
of
a
the correlation between the
e
and
only
this correlation requires
awards in the same case by the same arbitrator for both types
38
of
arbitration.
Overall,
substantial progress has been made in analyzing the decision
processes of arbitrators.
behavior in conventional
Not
only were distinct models of
and final-offer
arbitrator
arbitration identified, but
a
substantial degree of underlying consistency was found in the constructs
arbitrators use to make decisions in different settings.
In
addition,
the
study has demonstrated the value of using data derived from carefully designed
simulations
in
analyzing the behavior
further research are apparent.
of
arbitrators.
For e;;ample,
fi
number of areas
for'
since the arbitrator decision
process is likely to be central to the process of collective bargaining where
arbitration is the dispute settlement mechanism,
integrate the results
analysis
it
of
is clear
be useful
to
of
it
would be useful
to
studies such as this into theoretical and empirical
bargaining in an environment that includes arbitration.
that arbitrators differ
in
their decision processes,
Finally,
and it would
investigate both the degree to which there are such differences
and how these differences affect the bargaining process.
~9
REFERENCES
Anderson, John C. and Thomas h, kochan. "Impasse Procedures in the Canadian
Federal Service," Industrial ana Lac or Relation! Aft' jew 30 (April I'???):
282-301
Ashenfelter, Orlev and David E. Bloom.
and Evidence," Ater i can tconoB c
i
"Models of Arbitrator Behavior: Theory
e c
e w 74
(March 1964): 111-124.
A'
i
Barerman, Max H. and Henry S. Farber. "Arbitrator Decision Making: When are
in
Final O-fters Importanf^" Industrial and Labor Relations Rey len
press.
,
Bazerman, Max H. "Norms of Distributive Justice in Interest Arbitration,"
in press.
Industrial and Labor Relations Rey len
,
Bronwyn H. Hall, and Robert E. Hall. "Estimation and
Berndt, Ernst K.
Inference in Nonlinear Structural Models," Annals of Econotic and Social
Heasuretent 3/4 (1974): 653-665.
,
Bloom,
David
E.
L. Cavanaugh. "An Analysis of the Selection of
Harvard University, Department of Economics, mimeo (June
and Christopher
Arbitrators,"
1984).
Bonn,
L. "Arbitration: An Alternative System for Handling Contract Related
Disputes," Adainistrative Science Quarterly 17 (1972): 254-264.
R.
Crawford, Vincent P. "On Compulsory Arbitration Schemes," Journal of Political
Econoty 87 (February 1979): 131-159.
Farber, Henry S.
Resolution
Analysis of Final-Offer Arbitration," Journal of Conflict
(December 1980).
"An
Farber, Henry S. "Spl i tt ng-the-Di f erence in Interest Arbitration,"
Industrial and Labor Relations Revien 35 (April 1981): 70-77.
Farber, Henry S. and Harry C. Katr. "Interest Arbitration, Outcomes, and the
Incentive to Bargain." Industrial and Labor Relations Reviet^ 33 (October
1979): 55-63.
Feigenbaum, Charles. "Final
Industrial Relations
Offer Arbitration: Better Theory Than Practice,"
(October 1975): 311-317.
14
Feuille, Peter. "Final Offer Arbitration and the Chilling Effect," Industrial
Relations 14 (October 1975): 302 -310.
Gallagher, Daniel and M. D. Chaubey. "Impasse resolution and Tri-Offer
Arbitration in Iowa," Industrial Relations 21 (Spring 1982): 129-148.
Kochan, Thomas A. and Jean Bader schnei der
"Determinants of Reliance on
Impasse Procedures: Police and Firefighters in New York State."
Industrial and Labor Relations Reyien 31 (July 1978): 431-440.
.
4
Neale,
Margaret A. and Max H, Ba:erman. "The Role o-f Perspective Taking
Ability in Negotiating Under Different Forms of Arbitration," Iiidustrial
1983): 378-388.
arid Lsbcr Relations Reviet^ 36 (April
Northrup, Herbert R. Cotpulsory Ar b t r at i on arid Ooverhteitt Iri t e r
Labor Disputes. Washington, D.C. Labor Policy Association,
i
Not:,
Star
I:
i'eri 1 1 cti
in
1966.
William W. and Frederick A, Starke. "Final Offer versus Convnetional
Arbitration as Means of Conflict Management," Adim i str at i\'e Science
Quarterly 23 (June 1978): 189-203.
Frederick A. and William W. Notz. "Pre- and Post-Intervention Effects
Conventional vs. Final Offer Arbitration," Acadety of Hanagetent
Journal 24 (1981): 832-850.
e,
of
Stevens, Carl M. "Is Compulsory Arbitration Compatible with Bargaining'!'"
Industrial Relations 5 (1966): 38-50.
Wheeler, Hoyt N. "Closed Offer: A;i alternative to Final-Offer Selection,"
Industrial Relations 16 (1977): 298-305,
Wheeler, Hoyt N. "Hqw Compulsory Arbitration Affects Compromise Activity,"
Industrial Relations 17 (1978): 80-84.
-
Table
(Di
Van abl e
PW
Means and Standard Deviations of Data
1.
Mean
Description
chotomous variables
=0 otherwise)
log
of
(s.d.
;
2.08
present wage
(.392)
loQ di-ff
.0966
(.0242)
between award and PW
FOA cases for Managenment
FOA
proportion
INF
i
COMP
comparable arbitrated settlements
LM
log diff between local
n-f
1
ati on
o-f
.644
.110
.0285)
rate
wage and PW
100
(.0281:
.
.00960
(.101)
NW
log diff
between national wage and PW
.00520
(.0214)
CONDB
=1
if
company in terrible or poor shape
.405
CONDG
=1
if
company in good or excellent shape
.398
MFD
log diff
between man.
UFO
log diff
between union final offer and PW
AFO
loQ diff
between ave,
DFO
log difference between final
N=1522
final
final
offer and PW
offer and PW
offers
.0729
(.0289)
.140
(.0282)
.107
(.0252)
.0673
(.0271)
Estimates
of
Table 2:
Exolicit Models of Arbitrator Decisions:
Conventional
Determinants
of
Unconstrained Model
Final-offer
P
-P,
V
Constant
.0300
(.00755)
-.00368
.218
(.0311)
-.0241
0243)
COMP
.434
(.0225)
.416
(.0341)
.0180
(.0329)
LW
.0246
(.00650)
.0291
(.00822)
-.00455
.266
(.0311)
.279
(.0504:
-.0134
PW
.00308
(.00191)
.00328
(.00256)
-
CONDB
-.0190
-.0256
(.00182)
(.00280)
00660
(.00246)
.00664
(.00184)
.00370
(.00224)
.00294
(.00190)
.0263
(.00575)
INF
194
NW
C0ND6
Weioht on
FT
Y
'
(.00690)
(.0298)
(.00799)
(.0477)
0196
(.00241)
.
.
(H
.750
(.0515)
1.69
673)
(
.
Relative weioht on the manaoement offer
.673
(.0441)
6
Covariance matrix
.000449
(.0000229)
.000346
(.0000412)
.00000898
(.00000372)
-.421
.0107
^e
(.127)
(.
155)
.818
c^
(.032'')
1617.3
In (L)
The numoers in parentheses are asymptotic standard errors.
IS the
:f
correlation between £
and £
refers to the correlation between a and
.
either £
or £
depending on the column.
N=1522
Note:
.
,
/>
Table 3:
Estimates ot Explicit Models d Arbitrator Decisions: Constrained Models
Constrained #1
Constrained #2
Const rai ned #3
FGh
FOA
CONV
CONV
CONV
FOA
iF'
Determinants o-f
^
Summar-y'
of
Table
Moaei
4.
Per-forinance
CONSTRAINTS
MODEL
*>
OF
PARMS
unconstrained
constrained
LOG
1617.3
#1
c
c
c-f
cM-fWc-f
14
constrained #2
1536.
1445.7
constrained #3
17
m
PuJ
1608.
L
TaDle
5:
Case
Y
1
Predicted values
(Y
e^
ec
or
V
Y
,
ec
Y
)
ec
,
and tneir Ditterences tdt
ef
Lase
Each Scenario
Y
(Y
e^
pf
)
ec
3
TDfi D
D
DM Mae DO
laleJ|tf,c,FMFW
lU
Lib-26-67