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The strike experience model: Adaptive expectations applied to strikes
THE STRIKE EXPERIENCE MODEL: ADAPTIVE EXPECTATIONS APPLIED TO STRIKES Rem
0. Kymn
and Catherine
Since 1941. the BLS has reported annual figures on work time lost due to strikes [143. Several authors have attempted to translate the time loss measure into a measure of economic losses [3, 6, 10, 111. For example, the authors of this paper have elsewhere developed a measure of economic loss due to strikes in the steel industry for the period 1950-72 [S], in which we attempted to identify the loss due to unused labor as well as to other resources. It is the prospect of inflicting economic losses that makes the strike or threat of a strike such an important instrument in collective bargaining.
A. Palomba
the model as a diagnostic tool, presenting empirical evidence suggesting the value of various measurements as indicators of generalized economic disorder due to strikes. This is using "generalized" in the sense of spreading the strike effects throughout the economic system from a specific point of origin. The empirical evidence we cite comes from the steel industry, which we examine as a case study. The paper is divided into three major sections: Section 1 reports the strike experience model; Section 2 applies the model to the steel industry; and Section 3 contains conclusions.
In this paper a strike experience model is developed which incorporates the concept of adaptive expectations. In the models expected strike costs become a function of (are adapted to) actual strike costs. We argue that expected strike costs figure importantly in the behavior of those involved in negotiations. In addition, we develop
II.
The Strike
Experience
-1:
The strike experience presses expected strike of actual strike costs the following manner :
model which excosts in terms was developed in
cost8 and S* for the expected Let S stand for actual strike of s. Denote that the rate of change in t as time. Assume strike costa and it8 expected level are d log s/dt and d log then in an exact analogy to the adaptive model2 we have: d
(d
dt
= B (d
log dt
S*)
d log
S* then dt
log
8 _ tt log
S*)
dt
, where
coefficient. Let E*
=
-&
(E*)
An
Extemsioe of 88 Adaptive EJcpectatbes hdel to strike cost An8lyBis
= 6 d iFg
135
’
- Et).
f3 is
level actual S*/dt.
an expecta-
136
VOLUMEXV,No.l&
Solving
this
linear
first
2
order differential
JBE
equation
E* I CemBt + BeBBt / eBt ( d 'd"t" '1 dt,
in E*, we get
where C is an integration
constant. We are only intereted in measuring E* for an finite Let the upper and lower limit of time be T and R. Then: T El*
-f3t
T
-Be +Be
= Ce R
R
E*(T)
-
E*(R)
/ v e8t
0
') dt]
If we choose a time at which we can approximately and set R = 0 as the origin, then E* (R) = 0 and =
T:
E*(T) T
+ Be BT Let 0
s
1oc3 z eBt 0
assume E* (R) = 0
+ Ce-flT + Be B
-C
but for E*(R) = 0, R=O, therefore
and
R
[Ce-Bt + Be -Bt / T @et(d log ') at]
=
[Ce-BR + Be -eR/ t eBt (d 'if
E*(T)
T
(d log ') dt dt
0
A
log
s
we must have C = 0. So: (t),
when A t = 1 and A log S(t)=
(t)
(t-1) A log S(t)
T = C efit 1
A log S(t)
+ A log S.
But A log S(o) = 0 by assumption of the chosen time origin. we write: T E*(T) = BgT C e Bt A log S (t) . . . . . . . . . . . . . . . . . . 1 Finally finite
period.
we have succeeded actual strike costs.
in expressing expectations For computational purposes,
Therefore (A)
in terms of the following
JBE
SPRING/SUMMER1986
is more
If
convenient
E*(T)
= Be -ST
it
assumed
is
expected
level
equation
(B),
E**(T)=9&ST
The economic
than
equation
T-l c 1 that are
eat
the ds dt
by denoting
T-l C 1
eBt
interpretation
(A):
A
rate
and
log
of
dS* -dt E**
S(t)
change
+ eST
in
respectively,
dS* = dt
A S(t)
of
137
We can hypothesize that the variables listed below would compose the vector of determinants which affect the duration Of a strike which in turn would comprise the main component of strike costs, given the number of workers involved.
actual
S(T)
strike
...
costs
we have,
in
(B)
and its
parallel
to
9
+ egT
the
Alog
cc>
A S(T) . . . . . . . . . . . .
strike
experience
post, union etc.
model
(11) the weight leaders
in
follows.
relative to the other industries,
3. Union strength: A vector representing (12) the size of union membership, (13) the age composite of union members, (14) union fund, etc.
1. Issues
and differences in the offered tens of labor contract between the negotiating parties: A vector representing (1) the amount of wage increases, (2) shift wage dffferentials (3) on-the-job grievance settling procedures, fringe benefits such as (4) pensions, (5) vacations, (6) retirements, etc.
2. Union Leadership: A vector representing (7) age, (8) union experience, (9) years of service of the union leaders in the present post, (10) the proportion of votes received for being elected to the
4. General economic conditions: A vector representing (15) the Consumer Price Index (CPI) as an index of purchasing power of wages, (16) unem ployment in the economy, (17) total man-hours worked, (18) total overtime (19) productivity hours worked, ciiinges, etc. 5. National and international politicalsocial conditions: A vector representing (20) months left until government election, (21) negotiations in times of war or post-war, etc.
VOLUMEXV,No.l&
138 6. World
and domestic market conditions of the cossnodfty that the industry produces: A vector representing (22) import and (23) export elasticities. (24) elastfcities of demand and (25) supply, (26) the world market price of the comnodfty, etc.
7. Pattern-setting
labor contracts settled in other industries: A vector representing (27) major characteristics If labor contract(s) settled in industries other than the one under investigation prior to the negotiation time. etc.
8. Management
attitude: A vector representing (28) profit of the firms in the industry ta%es, (29) capital expansion (30) size of pre-strike and strike inventory build-up, etc.
rate after rate, post-
Government policy: A vector representing (31) wafting time before entering into arbitration, (32) intensity of arbitration, etc. Although not intended to be exhaustive, it is thought that the listed varfables form the vector of detenfnants which affect the duration of the strike and therefore strike costs. Indeed the investigators strongly suspect that the fnvolved parties usually go to the negotiating table with a fairly accurate "feel" (prediction with a high probabflfty of being accurate) about the duration of a strike, such as:
(a)
easy settlement duration or not
(a strike strike),
of zero
b)
2
a brief show sides (a strike
JBE of of
strength on both short duration),
(cl
a tough negotiation several weeks duration),
(d)
a very difficult head (a strike tion).
of
(a
strike or
and hard prolonged
of
road adura-
It is likely that the negotiating parties' "feel" about the possible duration of a strike ahead, including one of zero duration, would be based on intuition developed from their observations of the host of variables listed above. When a new labor contract negotiation appears on the horizon, the prospective negotfating parties use their intuition to formulate their negotiation strategies. When an industry suffers a work stoppage, employees of all categories, managers, and owners of capital, land, and other forms of resources are affected, as are closely related industries. This effect in the aggregate constitutes the economic cost of a strike, and this economic cost is viewed and utilized as a tool to fnduce the other party to accept or come closer to accepting the offer given in labor negotiations. This study postulates that when a strike starts the party fnvolved tries to learn from past experfence -- success or failure -- of strike strategies and behaves accordingly. We can thus identify strike costs with past experience of strike strategies and our strike experience model, mainly couched under the term "adaptive expectations," can be accorded a microeconomic fnterpretation. While tations quantity'
the variables in adaptive expececonomic represent may any [1,2,4,5,9], we restrict our
SPRING/SUMMER
JBE
attention to adaptive expectations concerning strike costs. In the face of uncertainty, the party involved in a strike is postulated to formulate expectations of strike costs based on experience embodying observations of the list of determinants presented above. If his expectations are incorrect, he will adjust them to reduce the discrepancy between actual and expected strike costs. The value of g, the expectation coefficient, is a measure of the adjustment of expectations. Let the actual change in strike dS and dS* and let dT dt that the party in at a disequilibrium will change. We greater
and expected rates of costs be, respectively, dS* = E*. Assume also dt a strike is originally point so that E* assume that if dS is dt E* will rise. Likewise
than g*, dt * will fall if dS is below dS*. Expected dT dt strike costs do not fall when actual costs are rising or vice versa. This is the Let X 'consistency' assumption. represent the disequilibrium differences and be defined as
a idS-p
(1)
.
dt Whenever a departure from equilibrium appears, it is assumed that the involved Party adjusts to disequilibrium by changing E*fC. This assumption is expressed by a first-order differential equation such as d/dt
(EM)
= BX
1986
efficient and X is the disequilibrium difference. The expression in (2) represents the formulation of a continuous strike experience model or a continuous adaptive expectations model.3 Transposing and approximating, we get from (2) the following expression, 0 = A(E**)/
g represents
the
CO-
(3)
There exist three possibilities starting from a disequilibrium point such as A. Suppose the involved party adjusted A to a', where dS equals dS*. In this dt dt case, B = 1. This is the case of "exact adjustment." Suppose, however, the individual attains a position short of A'. For any move away from A but not achieving A',
O<@
ObfiSl. It is easy to AE*+ = 0. This
see that b = 0 yields is the case of *static expectations.* If we exclude the possibility of overadjustment and adopt a dynamic strike experience model we have
(2) expectation
X.
Changes in (E**) over time can be represented by A instead of d/dt and the expectation coefficient B is expressed as a ratio. (3), then, is a discrete strike experience model or a discrete adaptive expectations model.
O
139
140
VOLUME
Also it is easy to see that g =-implies A= 0. This is the case of "perfect myopic foresight."
sent
From the above analysis, we can reprethe segment of overadjustment by
l<
f3 c QI.
If we include the possibility adjustment in a dynamic strike model we have o<
of overexperience
f3 < -.
It should be pointed out that f3 can vary from 0 to infinity without attaching any particular significance to the value of unity in a continuous model. Despite the intensive investigation of the properties of discrete adaptive expectations models and their widespread use in the empirical literature, certain aspects of adaptive expectations remain unclear. In particular, the meaning of 6, the expectation or adjustment coefficient, is quite unclear. The others behavior" ment -merit" --
question raised by Takayama and [5, 123, concerns what "rational would yield incomplete adjustnot reaching A' -- "overadjustmovement to the left of A'.
It has been argued that the degree of adjustment may depend upon benefits and costs associated with gathering the necessary information [7]. In the discrete adaptations model, it may well be the case that there exists symmetric lower and upper bounds on the value of beta. The exact l&cation of those bounds the benefits and costs depends upon associated with acquiring optimal infor-
XV, No. 1 & 2
JBE
mation necessary to adjust expectations based on the observations of the determinants listed previously. Changes in the benefits and costs of the search procedure will, of course, change these bounds, i.e., the required foregone benefits from the divergence between actual and expected strike costs that is optimal in the sense of net benefits. There may be a "region of rational behavior" with respect to values of g. optimal overadjustment or incomplete adjustment which is consistent with the net benefits from revising expectations. Consequently, it is not surprising to find many empirical estimates of the expectation coefficient values different from unity. It is to be expected. The concept of "learning" is distinct from the economics of information in the sense that the former is directly included in adaptive expectations hypotheses. When 0 4 B S for an equation of the form
xet= xet-1+B (xt-l-Xet-1). where Xet is the expected value of X in time t and beta is the expectation coefficient, an element of learning is already incorporated in the equation. If there is error between the actual and expected value of X in the previous time period, the party involved in a strike “learns" and will modify behavior. The economics of information, however, is part of the explanation of the speed and completeness of the adjustment.
II.
An Application of the Strike Experience Model to the Steel Industry
In order to utilize the model direct strike costs in the steel industry had to be estimated. As described elsewhere
SPRING/SUMMER1986
[8], this involved weighting man days lost due to strikes by the wages of production workers per man days worked and by value-added per man days worked. The resulting figures appear in Table I, column 1. As a first approach, the direct strike cost figures were then sorted into an ascending order starting from the lowest cost figure. The computational formula C was used to calculate E**. In this sorted method, the largest scale strike experience received the heaviest weight in the computation of the expectation series of the rate of changes in strike costs (E*
=5
in C).
In the computation of E* actual strike cost (S) was weighted by varying weights. The computation was such that the data point nearest to the current position was given the heaviest weight while the data points farthest away from the current position were given almost negligible weight. The weights diminished rapidly as the data points were removed from the current position. Since the series of S in our computations was sorted into an ascending order, the data on the largest scale strike was nearest the current position and consequently received the heaviest weight. The investigators felt that this type of sorting was justified since larger scale strikes may be retained more distinctly than smaller ones as a reference point by the negotiating parties. After the series of direct strike cost data S was sorted into an ascending order varying values of $ in the range of 5 = 0.1, 0.2, . . . 0.9, and 1.0 were assigned.
The next step was to integrate an indicator of a generalized disorder into the strike experience model. Three candidates were used initially. They are the series of MU (number of man-days idle during the year), P (man-days idle during the year as a percent of total working time), and A (man-days idle during the year per This data appears in worker involved). Table 1. The operation of such an integration was accomplished in the following manner: After the series of direct strike costs S was sorted into an ascending order, the series of S was matched with the corresponding series of MU, P, and A. Under the assigned values of g, the series of was converted to E** = dS*. dt Then the series of E* (expected values in changes in 5) was correlated with the matching order series of MU, P, and A. The results of these correlations are shown4 in Table 2. The correlation results show that the fit Rleasured in terms of p was the highest for MD, P, and A when beta was assigned the value of b - 0.1. When 8 = 0.1 the correlation coefficient between E* and P was approximately 0.9854 whereas the correlatin coefficients between E** and Ml and E* and A were 0.9778 and 0.9275, respectively. The values of the correlation coefficientsdeclined steadily although not sharply, as higher values of U were assigned. In all cases, the estimated correlation coefficients were found. to be statistically significant at the 95X level. As a second approach to the application of the strike experience model, E* was computed without sorting the S series into an ascending order. In this method, no particular weight was assigned to the
142
VOLUME
XV, No. 1 & 2
Table
JBE
1
DIRECT STRIKE COSTS IN STEEL AND GENERALIZED DISORDERINDICATORS
1950 to 1972
Direct Strike Costs in Steel
Year
1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972
Source:
18235.55 34265.13 1500080.69 38063.35 10480.07 57430.25 1011771.65 30050.64
12234.98 4553638.31 42039.88 13348.82
14226.19 31556.19 17507.01 39204.21 102886.17 58737.41 124389.54 66920.16 20900.20
63745.03 68628.38
U.S.
Department Basic of the Census, smry:
Number of Man-Days
Idle (thousands)
295.8 562.0 20400.0 521.6 174.8 759.1 11269.9 436.4 197.9 36637.0 471.5 224.5 194.5 285.1 181.1 342.4 798.3 498.5 1040.8 544.5 202.8 456.5 445.8
Man-Days Idle as Percent of Total Working Time
0.2 .3 12.5 .3 .l .4 6.3 .2 .l 24.4 0.3 .l .l .2 .l -2 .5 .3 .6 .3 .l .3 .3
Per Worker Involved
Wages of Productlol Worker Pe Man-Hour
3.8 4.3 38.5 3.9 4.0 1.6 23.1 6.2 4.0 71.3 8.0 7.0 6.1 9.0 6.9 12.5 19.6 12.3 21.8 11.0 9.7 17.4 20.8
of Labor, Bureau of Labor Statistics, Collective Bargaining Steel Industry, 1974 and U.S. Department of Commerce, Bureau Annual Survey of Manufacturers, 1949-1972.
1.71 1.89 2.06 2.21 2.23 2.33 2.53 2.71 2.92 3.08 3.10 3.21 3.29 3.36 3.42 3.54 3.62 3.70 3.93 4.15 4.35 4.71 5.22
JBE
SPRING/SUMMER
Table
1986
143
2
CORRELATIONS OF EXPECTED STRIKE COSTSAND GENERALIZEDDISORDERINDICATORS (Strike Costs Sorted by Size)
s
-ND
E
!!!
.I
.97775
.98543
.92746
-. 16022
.2
.97654
.98419
.92531
-.I6121
.3
.97525
.98286
.92359
-. 16125
.4
.97381
.98140
-92200
-. 16076
.5
.97224
-98984
.92042
-.15994
.6
.97057
.97820
.91885
-. 15892
.7
.96882
.97650
.91727
-. 15776
.8
.96705
.97479
.91570
-.15653
.9
.96527
.97308
-91415
-.15525
1.0
.96350
.97140
.91264
-. 15397
144
VOLUME
XV, No. 1 & 2
Table
JBE
3
CORRELATIONS OF EXPECTED STRIKE COSTSAND GENERALIZEDDISORDERINDICATORS (Strike Costs Chronological)
E
-MD
.l
.99151
.99252
.91974
.2
.97587
.97668
.92918
.3
.95691
.95770
.92975
.4
.93860
.93931
.92355
.5
.92174
.92234
.91376
.6
.90656
.90673
.90228
.7
.89200
.89235
.89021
.8
.87881
.87906
.87816
.9
.86660
.86676
.86648
1.0
.85530
.85539
.85536
SPRING/SUMMER
size of computing E**
the
strike.
I -dS* dt
In
this
method
of
'
the parties in the strike are assumed to remember the latest strike experience more distinctly than any other. It is assumed that in thfs second approach, the strike which is still "fresh" in regardless of the size of the memory, strike will act as a more powerful constituent of strike experience. Again varying values of 8 were assigned. The assigned values of 8 were 8 = 0.1, 0.2, . . . 0.9, and 1.0. Under the assignments of the varying values of 8, the series of S was again utilized to compute EH
I -dS* dt
,
with the use of formula C. Then the series of E* was correlated with the series of MB, P, and A. The correlation results are reported in Table 3. As in Table 2, the table reports the assigned values of 8 and lists the estimated correlation coefficients. The results of the correlations were not uniform anang the series of )ID, P, and A. Among the series, the estimated correlation coefficient between E* and P manifested the highest value with its estimate equal to 0.99252 when the asSigned value to beta was B = 0.10. Likewise, the estimated correlation coefficient between E* and W attained the highest value equal to .99151 when B = 0.10 was assigned. But the estimated Correlation coefficient between E* and A was highest with its estimate equal to 0.92975 when beta was assigned the
1986
value of $ = 0.3. The correlation coefficient between EM and both MU and P seemed to decline more rapidly compared to the case of E** and A as the assigned values were increased. The lowest estfmated values of the correlation coefffcients were observed when 8 = 1.0 was assfgned.to each of the series. Correlatfon was .8553, .8554 and .8554 for MU, P and A series, respectively. Comparing Tables 2 and 3, we observe that in both cases the estimated value of rho attained its highest value when E** and P are correlated with B = 1.0. In Table 3, the estimated value of rho was 0.99252 when E* was arranged in chronological order, but 0.98543 in Table 2 when E** was arranged by size of strikes. However, in Table 2 the correlations did not appear sensitive to the changes in the beta values as they did in Table 3. The estimated correlation coefficient decreased to 0.9714 for B = 1.0 in Table 2 in contrast to 0.85539 in Table 3 for 8 = 1.0. That is, in Table 2. the decline in the correlation coefficient was from 0.98543 to 0.9714, whereas the decrease in the estimated values of the correlation coefffcient was from 0.99252 to 0.85539 in Table 3. In all cases, the estimated correlation coefficients were statistically significant at the 95X level. As a contrast to the preceding experiY (wages of production workers ments, per man hour in current dollars) was used as an indicator of generalized disorder. Here the wage series (W) was sorted in the order corresponding to the ascending sequence of the S series, and the expected values of changes in the S series were computed with ten assignments of beta
146
VOLUME
values. The estimated correlation coefficients after correlating these two series are reported in Table 2. We observe that the estimated correlation coefficients range from -0.15397 to -0.16125. In general, the estimated correlation coefficients were observed to have very low values and wrong signs in all cases.
III.
Concluding
In industrial disputes, the possibility of inflicting economic cost is utilized as a primary tool of bargaining. We postulated that the negotiating parties attempt to learn about these costs from past strike experience utilizing the narrowly defined strike cost function. The strike experience model was developed by extending the adaptive form of expectations. Although our' strike experience model closely paralleled the adaptive form of expectations developed our numerical approximation by Cagan, formula differed from the one secured by Cagan.5 Our next step was to integrate an indicator that could serve as a signal of generalized disorder in the constructed model. We chose four possible candidates. They .were:
year
of (Ml
2. Man-days percent series)
JBE
idle during the of total working
3. Wan-days idle worker involved
during the (A series)
year as a time (P
year
per
4. Wages of production workers per manhour in current dollars (W series)
Remarks
In this study, we have concentrated on understanding strike behavior utilfzing the case of the steel industry as an example. Following estimation of the direct economic cost of strikes, a strike experience model was developed and applied to steel strike experience.
1. Number
XV, No. 1 & 2
man-days series)
idle
during
the
The criteria for selecting the above four series as possible candidates for an indicator of generalized disorder was based on their practicability and easy accessibility. Any of the first three series can be easily computed and monitored on a day to day basis. As expected the first three performed well as a possible indicator of generalized disorder. However, among the three, the second series (P) performed best. It is worth noting that the fourth series (W) will not serve as an indicator of generalized disorder as anticipated. In the cited integration operation, two different approaches were used. One approach was to investigate whether a strike experience "fresh" in memory will be used more distinctly as a reference point. Although both approaches yielded it was found that the good results, latter seemed to perform better relative to the former. This result seems to indicate that generally issues in industrial disputes "evolve" through a cumulative effect over time. The estimated value of the expectation coefficient was found to be 0.1 indicating that the time span of adjustment in strikes relative to the time path of strikes seemed to be relatively long.
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SPRING/SUMMER
For practical application the investigators recommend that man-days idle as a percent of total working time be adopted as an indicator of generalized disorder. The percentage should be computed on the basis of an annual rate leading to man-days idle during the year as a percent of total working time. We should note that the P series is the only indicator which can be overtly converted to an annual rate among the three series of MD, P and A. The recommended series is defined as the ratio of man-days idle to estimated average annual employment multiplied by total working days for the year in a striking industry.
1986
147
widely used and even adopted by Friedman in his calculation of permanent income. Concerning this point, refer to Friedman
151. ***** REFERENCES
1. Arrow,
K.J. and M. Nerlove. "A Note on Expectations and Stability," Econometrica, April 1958, Vol. 26, pp. 297-305.
NOTES
2. Cagan, P. "The Monetary Dynamics of Hyper-Inflation." in Studies in the Quantity Theory of Money (M. Friedman, ed.), Chicago: University of Chicago Press, 1956.
lKern 0. i(ymn and Catherine A. Palomba are from the Department of Economics, at West Virginia University.
3. Chamberlain, N.W. and J.M. Schflling. The Impact of Strikes, Harper and Brothers, 1954.
2This adaptive form of expectations closely aprallels the one originally developed by Cagan. However, the numerical approximation formula obtained in this paper is different from the one secured by Cagan. See Cagan [23.
4. Fisher, F.M. and P. Temin. "Regional Specialization and the Supply of Wheat in the United States, 19671974,” Review of Economics and Stastitics, May 1970, Vol. 52, pp. 134-147.
3Although different in notation, this expression parallels the adaptive form of expectations developed by Cagan. Refer to footnote 2.
5. Friedman, M. A Theory of the Consumption Function, Princeton, 1957.
l m*
4Such an estimation method is proven to be equivalent to the maximum likelihood estimation by Cagan. Refer to Cagan for the proof [23. 5The cited difference in the approximation formula is worth noting because Cagan's approxfmatin formula has been
6. Gahali, MA. "On Measuring Third Party Effects of a Strike," Western Economic Journal, June 1973. 7.
l(ymn, K.O. and W.P. Page. "A Microeconomic and Geometric Interpretation of Beta in Models of Discrete Adaptive Expectation," Review of Business and Economic Research, Spring
1978.
VOLUMEXV,No.1&2
148 8.
Kymn, K.O. and C. Palomba. "Annual Strike Costs in the Steel Industry, 1950 to 1972,” Department of Economics, West Virginia University.
9. Nerlove, H. Baltimore, IO.
The
Dynamics
of
11. Rehmus,
12.
Takayama, A. Mathematical Hinsdale, 1974.
13.
U.S.
Department of Conxnerce. Bureau of the Census, Annual Survey of Manufacturers, 1974-1972.
14.
U.S.
Department of Labor Statistics, Stoppages, annual.
15.
U.S.
Supply,
1956.
Palomba, N. and C. Palomba. "The Economic Costs of Strikes: A Suggested Measure," Mississippi Valley Journal of Business and Economics, Vol. X, No. 1, Fall 1974. C.M. "Measuring Strikes," Journal of tistical Association, 1962, pp. 53-57.
the Impact of American StaBusiness,
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Labor, Analysis
Economics,
Bureau of of Work
Department of Labor, Bureau of Labor Statistics, Collective Bargaininq Swmnary, Basic Steel Indus-
5,
1974.
0. Kymn
and Catherine
Since 1941. the BLS has reported annual figures on work time lost due to strikes [143. Several authors have attempted to translate the time loss measure into a measure of economic losses [3, 6, 10, 111. For example, the authors of this paper have elsewhere developed a measure of economic loss due to strikes in the steel industry for the period 1950-72 [S], in which we attempted to identify the loss due to unused labor as well as to other resources. It is the prospect of inflicting economic losses that makes the strike or threat of a strike such an important instrument in collective bargaining.
A. Palomba
the model as a diagnostic tool, presenting empirical evidence suggesting the value of various measurements as indicators of generalized economic disorder due to strikes. This is using "generalized" in the sense of spreading the strike effects throughout the economic system from a specific point of origin. The empirical evidence we cite comes from the steel industry, which we examine as a case study. The paper is divided into three major sections: Section 1 reports the strike experience model; Section 2 applies the model to the steel industry; and Section 3 contains conclusions.
In this paper a strike experience model is developed which incorporates the concept of adaptive expectations. In the models expected strike costs become a function of (are adapted to) actual strike costs. We argue that expected strike costs figure importantly in the behavior of those involved in negotiations. In addition, we develop
II.
The Strike
Experience
-1:
The strike experience presses expected strike of actual strike costs the following manner :
model which excosts in terms was developed in
cost8 and S* for the expected Let S stand for actual strike of s. Denote that the rate of change in t as time. Assume strike costa and it8 expected level are d log s/dt and d log then in an exact analogy to the adaptive model2 we have: d
(d
dt
= B (d
log dt
S*)
d log
S* then dt
log
8 _ tt log
S*)
dt
, where
coefficient. Let E*
=
-&
(E*)
An
Extemsioe of 88 Adaptive EJcpectatbes hdel to strike cost An8lyBis
= 6 d iFg
135
’
- Et).
f3 is
level actual S*/dt.
an expecta-
136
VOLUMEXV,No.l&
Solving
this
linear
first
2
order differential
JBE
equation
E* I CemBt + BeBBt / eBt ( d 'd"t" '1 dt,
in E*, we get
where C is an integration
constant. We are only intereted in measuring E* for an finite Let the upper and lower limit of time be T and R. Then: T El*
-f3t
T
-Be +Be
= Ce R
R
E*(T)
-
E*(R)
/ v e8t
0
') dt]
If we choose a time at which we can approximately and set R = 0 as the origin, then E* (R) = 0 and =
T:
E*(T) T
+ Be BT Let 0
s
1oc3 z eBt 0
assume E* (R) = 0
+ Ce-flT + Be B
-C
but for E*(R) = 0, R=O, therefore
and
R
[Ce-Bt + Be -Bt / T @et(d log ') at]
=
[Ce-BR + Be -eR/ t eBt (d 'if
E*(T)
T
(d log ') dt dt
0
A
log
s
we must have C = 0. So: (t),
when A t = 1 and A log S(t)=
(t)
(t-1) A log S(t)
T = C efit 1
A log S(t)
+ A log S
But A log S(o) = 0 by assumption of the chosen time origin. we write: T E*(T) = BgT C e Bt A log S (t) . . . . . . . . . . . . . . . . . . 1 Finally finite
period.
we have succeeded actual strike costs.
in expressing expectations For computational purposes,
Therefore (A)
in terms of the following
JBE
SPRING/SUMMER1986
is more
If
convenient
E*(T)
= Be -ST
it
assumed
is
expected
level
equation
(B),
E**(T)=9&ST
The economic
than
equation
T-l c 1 that are
eat
the ds dt
by denoting
T-l C 1
eBt
interpretation
(A):
A
rate
and
log
of
dS* -dt E**
S(t)
change
+ eST
in
respectively,
dS* = dt
A S(t)
of
137
We can hypothesize that the variables listed below would compose the vector of determinants which affect the duration Of a strike which in turn would comprise the main component of strike costs, given the number of workers involved.
actual
S(T)
strike
...
costs
we have,
in
(B)
and its
parallel
to
9
+ egT
the
Alog
cc>
A S(T) . . . . . . . . . . . .
strike
experience
post, union etc.
model
(11) the weight leaders
in
follows.
relative to the other industries,
3. Union strength: A vector representing (12) the size of union membership, (13) the age composite of union members, (14) union fund, etc.
1. Issues
and differences in the offered tens of labor contract between the negotiating parties: A vector representing (1) the amount of wage increases, (2) shift wage dffferentials (3) on-the-job grievance settling procedures, fringe benefits such as (4) pensions, (5) vacations, (6) retirements, etc.
2. Union Leadership: A vector representing (7) age, (8) union experience, (9) years of service of the union leaders in the present post, (10) the proportion of votes received for being elected to the
4. General economic conditions: A vector representing (15) the Consumer Price Index (CPI) as an index of purchasing power of wages, (16) unem ployment in the economy, (17) total man-hours worked, (18) total overtime (19) productivity hours worked, ciiinges, etc. 5. National and international politicalsocial conditions: A vector representing (20) months left until government election, (21) negotiations in times of war or post-war, etc.
VOLUMEXV,No.l&
138 6. World
and domestic market conditions of the cossnodfty that the industry produces: A vector representing (22) import and (23) export elasticities. (24) elastfcities of demand and (25) supply, (26) the world market price of the comnodfty, etc.
7. Pattern-setting
labor contracts settled in other industries: A vector representing (27) major characteristics If labor contract(s) settled in industries other than the one under investigation prior to the negotiation time. etc.
8. Management
attitude: A vector representing (28) profit of the firms in the industry ta%es, (29) capital expansion (30) size of pre-strike and strike inventory build-up, etc.
rate after rate, post-
Government policy: A vector representing (31) wafting time before entering into arbitration, (32) intensity of arbitration, etc. Although not intended to be exhaustive, it is thought that the listed varfables form the vector of detenfnants which affect the duration of the strike and therefore strike costs. Indeed the investigators strongly suspect that the fnvolved parties usually go to the negotiating table with a fairly accurate "feel" (prediction with a high probabflfty of being accurate) about the duration of a strike, such as:
(a)
easy settlement duration or not
(a strike strike),
of zero
b)
2
a brief show sides (a strike
JBE of of
strength on both short duration),
(cl
a tough negotiation several weeks duration),
(d)
a very difficult head (a strike tion).
of
(a
strike or
and hard prolonged
of
road adura-
It is likely that the negotiating parties' "feel" about the possible duration of a strike ahead, including one of zero duration, would be based on intuition developed from their observations of the host of variables listed above. When a new labor contract negotiation appears on the horizon, the prospective negotfating parties use their intuition to formulate their negotiation strategies. When an industry suffers a work stoppage, employees of all categories, managers, and owners of capital, land, and other forms of resources are affected, as are closely related industries. This effect in the aggregate constitutes the economic cost of a strike, and this economic cost is viewed and utilized as a tool to fnduce the other party to accept or come closer to accepting the offer given in labor negotiations. This study postulates that when a strike starts the party fnvolved tries to learn from past experfence -- success or failure -- of strike strategies and behaves accordingly. We can thus identify strike costs with past experience of strike strategies and our strike experience model, mainly couched under the term "adaptive expectations," can be accorded a microeconomic fnterpretation. While tations quantity'
the variables in adaptive expececonomic represent may any [1,2,4,5,9], we restrict our
SPRING/SUMMER
JBE
attention to adaptive expectations concerning strike costs. In the face of uncertainty, the party involved in a strike is postulated to formulate expectations of strike costs based on experience embodying observations of the list of determinants presented above. If his expectations are incorrect, he will adjust them to reduce the discrepancy between actual and expected strike costs. The value of g, the expectation coefficient, is a measure of the adjustment of expectations. Let the actual change in strike dS and dS* and let dT dt that the party in at a disequilibrium will change. We greater
and expected rates of costs be, respectively, dS* = E*. Assume also dt a strike is originally point so that E* assume that if dS is dt E* will rise. Likewise
than g*, dt * will fall if dS is below dS*. Expected dT dt strike costs do not fall when actual costs are rising or vice versa. This is the Let X 'consistency' assumption. represent the disequilibrium differences and be defined as
a idS-p
(1)
.
dt Whenever a departure from equilibrium appears, it is assumed that the involved Party adjusts to disequilibrium by changing E*fC. This assumption is expressed by a first-order differential equation such as d/dt
(EM)
= BX
1986
efficient and X is the disequilibrium difference. The expression in (2) represents the formulation of a continuous strike experience model or a continuous adaptive expectations model.3 Transposing and approximating, we get from (2) the following expression, 0 = A(E**)/
g represents
the
CO-
(3)
There exist three possibilities starting from a disequilibrium point such as A. Suppose the involved party adjusted A to a', where dS equals dS*. In this dt dt case, B = 1. This is the case of "exact adjustment." Suppose, however, the individual attains a position short of A'. For any move away from A but not achieving A',
O<@
ObfiSl. It is easy to AE*+ = 0. This
see that b = 0 yields is the case of *static expectations.* If we exclude the possibility of overadjustment and adopt a dynamic strike experience model we have
(2) expectation
X.
Changes in (E**) over time can be represented by A instead of d/dt and the expectation coefficient B is expressed as a ratio. (3), then, is a discrete strike experience model or a discrete adaptive expectations model.
O
139
140
VOLUME
Also it is easy to see that g =-implies A= 0. This is the case of "perfect myopic foresight."
sent
From the above analysis, we can reprethe segment of overadjustment by
l<
f3 c QI.
If we include the possibility adjustment in a dynamic strike model we have o<
of overexperience
f3 < -.
It should be pointed out that f3 can vary from 0 to infinity without attaching any particular significance to the value of unity in a continuous model. Despite the intensive investigation of the properties of discrete adaptive expectations models and their widespread use in the empirical literature, certain aspects of adaptive expectations remain unclear. In particular, the meaning of 6, the expectation or adjustment coefficient, is quite unclear. The others behavior" ment -merit" --
question raised by Takayama and [5, 123, concerns what "rational would yield incomplete adjustnot reaching A' -- "overadjustmovement to the left of A'.
It has been argued that the degree of adjustment may depend upon benefits and costs associated with gathering the necessary information [7]. In the discrete adaptations model, it may well be the case that there exists symmetric lower and upper bounds on the value of beta. The exact l&cation of those bounds the benefits and costs depends upon associated with acquiring optimal infor-
XV, No. 1 & 2
JBE
mation necessary to adjust expectations based on the observations of the determinants listed previously. Changes in the benefits and costs of the search procedure will, of course, change these bounds, i.e., the required foregone benefits from the divergence between actual and expected strike costs that is optimal in the sense of net benefits. There may be a "region of rational behavior" with respect to values of g. optimal overadjustment or incomplete adjustment which is consistent with the net benefits from revising expectations. Consequently, it is not surprising to find many empirical estimates of the expectation coefficient values different from unity. It is to be expected. The concept of "learning" is distinct from the economics of information in the sense that the former is directly included in adaptive expectations hypotheses. When 0 4 B S for an equation of the form
xet= xet-1+B (xt-l-Xet-1). where Xet is the expected value of X in time t and beta is the expectation coefficient, an element of learning is already incorporated in the equation. If there is error between the actual and expected value of X in the previous time period, the party involved in a strike “learns" and will modify behavior. The economics of information, however, is part of the explanation of the speed and completeness of the adjustment.
II.
An Application of the Strike Experience Model to the Steel Industry
In order to utilize the model direct strike costs in the steel industry had to be estimated. As described elsewhere
SPRING/SUMMER1986
[8], this involved weighting man days lost due to strikes by the wages of production workers per man days worked and by value-added per man days worked. The resulting figures appear in Table I, column 1. As a first approach, the direct strike cost figures were then sorted into an ascending order starting from the lowest cost figure. The computational formula C was used to calculate E**. In this sorted method, the largest scale strike experience received the heaviest weight in the computation of the expectation series of the rate of changes in strike costs (E*
=5
in C).
In the computation of E* actual strike cost (S) was weighted by varying weights. The computation was such that the data point nearest to the current position was given the heaviest weight while the data points farthest away from the current position were given almost negligible weight. The weights diminished rapidly as the data points were removed from the current position. Since the series of S in our computations was sorted into an ascending order, the data on the largest scale strike was nearest the current position and consequently received the heaviest weight. The investigators felt that this type of sorting was justified since larger scale strikes may be retained more distinctly than smaller ones as a reference point by the negotiating parties. After the series of direct strike cost data S was sorted into an ascending order varying values of $ in the range of 5 = 0.1, 0.2, . . . 0.9, and 1.0 were assigned.
The next step was to integrate an indicator of a generalized disorder into the strike experience model. Three candidates were used initially. They are the series of MU (number of man-days idle during the year), P (man-days idle during the year as a percent of total working time), and A (man-days idle during the year per This data appears in worker involved). Table 1. The operation of such an integration was accomplished in the following manner: After the series of direct strike costs S was sorted into an ascending order, the series of S was matched with the corresponding series of MU, P, and A. Under the assigned values of g, the series of was converted to E** = dS*. dt Then the series of E* (expected values in changes in 5) was correlated with the matching order series of MU, P, and A. The results of these correlations are shown4 in Table 2. The correlation results show that the fit Rleasured in terms of p was the highest for MD, P, and A when beta was assigned the value of b - 0.1. When 8 = 0.1 the correlation coefficient between E* and P was approximately 0.9854 whereas the correlatin coefficients between E** and Ml and E* and A were 0.9778 and 0.9275, respectively. The values of the correlation coefficientsdeclined steadily although not sharply, as higher values of U were assigned. In all cases, the estimated correlation coefficients were found. to be statistically significant at the 95X level. As a second approach to the application of the strike experience model, E* was computed without sorting the S series into an ascending order. In this method, no particular weight was assigned to the
142
VOLUME
XV, No. 1 & 2
Table
JBE
1
DIRECT STRIKE COSTS IN STEEL AND GENERALIZED DISORDERINDICATORS
1950 to 1972
Direct Strike Costs in Steel
Year
1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972
Source:
18235.55 34265.13 1500080.69 38063.35 10480.07 57430.25 1011771.65 30050.64
12234.98 4553638.31 42039.88 13348.82
14226.19 31556.19 17507.01 39204.21 102886.17 58737.41 124389.54 66920.16 20900.20
63745.03 68628.38
U.S.
Department Basic of the Census, smry:
Number of Man-Days
Idle (thousands)
295.8 562.0 20400.0 521.6 174.8 759.1 11269.9 436.4 197.9 36637.0 471.5 224.5 194.5 285.1 181.1 342.4 798.3 498.5 1040.8 544.5 202.8 456.5 445.8
Man-Days Idle as Percent of Total Working Time
0.2 .3 12.5 .3 .l .4 6.3 .2 .l 24.4 0.3 .l .l .2 .l -2 .5 .3 .6 .3 .l .3 .3
Per Worker Involved
Wages of Productlol Worker Pe Man-Hour
3.8 4.3 38.5 3.9 4.0 1.6 23.1 6.2 4.0 71.3 8.0 7.0 6.1 9.0 6.9 12.5 19.6 12.3 21.8 11.0 9.7 17.4 20.8
of Labor, Bureau of Labor Statistics, Collective Bargaining Steel Industry, 1974 and U.S. Department of Commerce, Bureau Annual Survey of Manufacturers, 1949-1972.
1.71 1.89 2.06 2.21 2.23 2.33 2.53 2.71 2.92 3.08 3.10 3.21 3.29 3.36 3.42 3.54 3.62 3.70 3.93 4.15 4.35 4.71 5.22
JBE
SPRING/SUMMER
Table
1986
143
2
CORRELATIONS OF EXPECTED STRIKE COSTSAND GENERALIZEDDISORDERINDICATORS (Strike Costs Sorted by Size)
s
-ND
E
!!!
.I
.97775
.98543
.92746
-. 16022
.2
.97654
.98419
.92531
-.I6121
.3
.97525
.98286
.92359
-. 16125
.4
.97381
.98140
-92200
-. 16076
.5
.97224
-98984
.92042
-.15994
.6
.97057
.97820
.91885
-. 15892
.7
.96882
.97650
.91727
-. 15776
.8
.96705
.97479
.91570
-.15653
.9
.96527
.97308
-91415
-.15525
1.0
.96350
.97140
.91264
-. 15397
144
VOLUME
XV, No. 1 & 2
Table
JBE
3
CORRELATIONS OF EXPECTED STRIKE COSTSAND GENERALIZEDDISORDERINDICATORS (Strike Costs Chronological)
E
-MD
.l
.99151
.99252
.91974
.2
.97587
.97668
.92918
.3
.95691
.95770
.92975
.4
.93860
.93931
.92355
.5
.92174
.92234
.91376
.6
.90656
.90673
.90228
.7
.89200
.89235
.89021
.8
.87881
.87906
.87816
.9
.86660
.86676
.86648
1.0
.85530
.85539
.85536
SPRING/SUMMER
size of computing E**
the
strike.
I -dS* dt
In
this
method
of
'
the parties in the strike are assumed to remember the latest strike experience more distinctly than any other. It is assumed that in thfs second approach, the strike which is still "fresh" in regardless of the size of the memory, strike will act as a more powerful constituent of strike experience. Again varying values of 8 were assigned. The assigned values of 8 were 8 = 0.1, 0.2, . . . 0.9, and 1.0. Under the assignments of the varying values of 8, the series of S was again utilized to compute EH
I -dS* dt
,
with the use of formula C. Then the series of E* was correlated with the series of MB, P, and A. The correlation results are reported in Table 3. As in Table 2, the table reports the assigned values of 8 and lists the estimated correlation coefficients. The results of the correlations were not uniform anang the series of )ID, P, and A. Among the series, the estimated correlation coefficient between E* and P manifested the highest value with its estimate equal to 0.99252 when the asSigned value to beta was B = 0.10. Likewise, the estimated correlation coefficient between E* and W attained the highest value equal to .99151 when B = 0.10 was assigned. But the estimated Correlation coefficient between E* and A was highest with its estimate equal to 0.92975 when beta was assigned the
1986
value of $ = 0.3. The correlation coefficient between EM and both MU and P seemed to decline more rapidly compared to the case of E** and A as the assigned values were increased. The lowest estfmated values of the correlation coefffcients were observed when 8 = 1.0 was assfgned.to each of the series. Correlatfon was .8553, .8554 and .8554 for MU, P and A series, respectively. Comparing Tables 2 and 3, we observe that in both cases the estimated value of rho attained its highest value when E** and P are correlated with B = 1.0. In Table 3, the estimated value of rho was 0.99252 when E* was arranged in chronological order, but 0.98543 in Table 2 when E** was arranged by size of strikes. However, in Table 2 the correlations did not appear sensitive to the changes in the beta values as they did in Table 3. The estimated correlation coefficient decreased to 0.9714 for B = 1.0 in Table 2 in contrast to 0.85539 in Table 3 for 8 = 1.0. That is, in Table 2. the decline in the correlation coefficient was from 0.98543 to 0.9714, whereas the decrease in the estimated values of the correlation coefffcient was from 0.99252 to 0.85539 in Table 3. In all cases, the estimated correlation coefficients were statistically significant at the 95X level. As a contrast to the preceding experiY (wages of production workers ments, per man hour in current dollars) was used as an indicator of generalized disorder. Here the wage series (W) was sorted in the order corresponding to the ascending sequence of the S series, and the expected values of changes in the S series were computed with ten assignments of beta
146
VOLUME
values. The estimated correlation coefficients after correlating these two series are reported in Table 2. We observe that the estimated correlation coefficients range from -0.15397 to -0.16125. In general, the estimated correlation coefficients were observed to have very low values and wrong signs in all cases.
III.
Concluding
In industrial disputes, the possibility of inflicting economic cost is utilized as a primary tool of bargaining. We postulated that the negotiating parties attempt to learn about these costs from past strike experience utilizing the narrowly defined strike cost function. The strike experience model was developed by extending the adaptive form of expectations. Although our' strike experience model closely paralleled the adaptive form of expectations developed our numerical approximation by Cagan, formula differed from the one secured by Cagan.5 Our next step was to integrate an indicator that could serve as a signal of generalized disorder in the constructed model. We chose four possible candidates. They .were:
year
of (Ml
2. Man-days percent series)
JBE
idle during the of total working
3. Wan-days idle worker involved
during the (A series)
year as a time (P
year
per
4. Wages of production workers per manhour in current dollars (W series)
Remarks
In this study, we have concentrated on understanding strike behavior utilfzing the case of the steel industry as an example. Following estimation of the direct economic cost of strikes, a strike experience model was developed and applied to steel strike experience.
1. Number
XV, No. 1 & 2
man-days series)
idle
during
the
The criteria for selecting the above four series as possible candidates for an indicator of generalized disorder was based on their practicability and easy accessibility. Any of the first three series can be easily computed and monitored on a day to day basis. As expected the first three performed well as a possible indicator of generalized disorder. However, among the three, the second series (P) performed best. It is worth noting that the fourth series (W) will not serve as an indicator of generalized disorder as anticipated. In the cited integration operation, two different approaches were used. One approach was to investigate whether a strike experience "fresh" in memory will be used more distinctly as a reference point. Although both approaches yielded it was found that the good results, latter seemed to perform better relative to the former. This result seems to indicate that generally issues in industrial disputes "evolve" through a cumulative effect over time. The estimated value of the expectation coefficient was found to be 0.1 indicating that the time span of adjustment in strikes relative to the time path of strikes seemed to be relatively long.
JBE
SPRING/SUMMER
For practical application the investigators recommend that man-days idle as a percent of total working time be adopted as an indicator of generalized disorder. The percentage should be computed on the basis of an annual rate leading to man-days idle during the year as a percent of total working time. We should note that the P series is the only indicator which can be overtly converted to an annual rate among the three series of MD, P and A. The recommended series is defined as the ratio of man-days idle to estimated average annual employment multiplied by total working days for the year in a striking industry.
1986
147
widely used and even adopted by Friedman in his calculation of permanent income. Concerning this point, refer to Friedman
151. ***** REFERENCES
1. Arrow,
K.J. and M. Nerlove. "A Note on Expectations and Stability," Econometrica, April 1958, Vol. 26, pp. 297-305.
NOTES
2. Cagan, P. "The Monetary Dynamics of Hyper-Inflation." in Studies in the Quantity Theory of Money (M. Friedman, ed.), Chicago: University of Chicago Press, 1956.
lKern 0. i(ymn and Catherine A. Palomba are from the Department of Economics, at West Virginia University.
3. Chamberlain, N.W. and J.M. Schflling. The Impact of Strikes, Harper and Brothers, 1954.
2This adaptive form of expectations closely aprallels the one originally developed by Cagan. However, the numerical approximation formula obtained in this paper is different from the one secured by Cagan. See Cagan [23.
4. Fisher, F.M. and P. Temin. "Regional Specialization and the Supply of Wheat in the United States, 19671974,” Review of Economics and Stastitics, May 1970, Vol. 52, pp. 134-147.
3Although different in notation, this expression parallels the adaptive form of expectations developed by Cagan. Refer to footnote 2.
5. Friedman, M. A Theory of the Consumption Function, Princeton, 1957.
l m*
4Such an estimation method is proven to be equivalent to the maximum likelihood estimation by Cagan. Refer to Cagan for the proof [23. 5The cited difference in the approximation formula is worth noting because Cagan's approxfmatin formula has been
6. Gahali, MA. "On Measuring Third Party Effects of a Strike," Western Economic Journal, June 1973. 7.
l(ymn, K.O. and W.P. Page. "A Microeconomic and Geometric Interpretation of Beta in Models of Discrete Adaptive Expectation," Review of Business and Economic Research, Spring
1978.
VOLUMEXV,No.1&2
148 8.
Kymn, K.O. and C. Palomba. "Annual Strike Costs in the Steel Industry, 1950 to 1972,” Department of Economics, West Virginia University.
9. Nerlove, H. Baltimore, IO.
The
Dynamics
of
11. Rehmus,
12.
Takayama, A. Mathematical Hinsdale, 1974.
13.
U.S.
Department of Conxnerce. Bureau of the Census, Annual Survey of Manufacturers, 1974-1972.
14.
U.S.
Department of Labor Statistics, Stoppages, annual.
15.
U.S.
Supply,
1956.
Palomba, N. and C. Palomba. "The Economic Costs of Strikes: A Suggested Measure," Mississippi Valley Journal of Business and Economics, Vol. X, No. 1, Fall 1974. C.M. "Measuring Strikes," Journal of tistical Association, 1962, pp. 53-57.
the Impact of American StaBusiness,
JBE
Labor, Analysis
Economics,
Bureau of of Work
Department of Labor, Bureau of Labor Statistics, Collective Bargaininq Swmnary, Basic Steel Indus-
5,
1974.