Learning from Interest Arbitration: The Next Round

Learning from Interest Arbitration: The Next RoundAuthor(s): Craig A. Olson and Barbara L. RauSource: Industrial and Labor Relations Review, Vol. 50, No. 2 (Jan., 1997), pp. 237-251Published by: Cornell University, School of Industrial & Labor RelationsStable URL: http://www.jstor.org/stable/2525084 .

Accessed: 28/06/2014 19:22

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Cornell University, School of Industrial & Labor Relations is collaborating with JSTOR to digitize, preserveand extend access to Industrial and Labor Relations Review.

http://www.jstor.org

This content downloaded from 91.213.220.103 on Sat, 28 Jun 2014 19:22:57 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=cschool

http://www.jstor.org/stable/2525084?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


LEARNING FROM INTEREST ARBITRATION: THE NEXT ROUND

CRAIG A. OLSON and BARBARA L. RAU-*

In final offer arbitration the decision of the arbitrator provides the parties with information about the preferences of the arbitrator that is not available prior to the award. Using data from Wisconsin teacher negotiations from 1977 to 1986, the authors find that the information contained in an award altered the parties' expectations about the arbitrator's preferences and influenced the subsequent negotiated settlement. The negotiated settlement following an award was higher when the union's final offer was selected than when the employer's offer was selected. In the round following an award, the variance in negotiated settlements declined, and the wage structure toward which the settlements converged was one that conformed with the arbitrator's views of fairness.

A fundamental issue that has interested researchers studying the bargaining

process is the relationship between bilat- eral negotiated settlement outcomes and the dispute settlement procedure the parties agree to use if negotiations between

*Craig Olson is Wolfe Professor of Business Re- search and Professor of Business and Industrial Rela- tions at the School of Business and Industrial Rela- tions Research Institute, University of Wisconsin- Madison. Barbara Rau is Assistant Professor of Indus- trial Relations at the School of Management and Labor Relations at Rutgers University. Support for this research was provided by the Vilas Foundatioin at the University of Wisconsin, the Industrial Relations Section at Princeton University, and the National Science Foundation (SBR-9225016). An earlier ver- sioIn of this paper was titled "Negotiated Settlements and Learning from the Arbitration Experience." Helpful comments were provided by seminar partici- pants at Columbia University, MIT, the University of Illinois, the University of Maryland, Princeton- Uni- versity, and Cornell University.

them fail. This relationship is important because the dispute settlement procedure that the parties hold in reserve-a strike, arbitration, or litigation, for example-af- fects their relative bargaining power and their expectations about the settlement terms that can be agreed to without resort- ing to that procedure and incurring the costs associated with it (Farber and Katz 1979). Bargaining under the threat of arbitration provides a fruitful setting for studying the impact of dispute settlement procedures on negotiated settlements. Arbitra- tion systems are simpler and easier to un- derstand than strikes because they operate under a set of well-defined procedures and rules, with the outcome usually decided by

The data used in this paper are available from the first author at the University of Wisconsin, School of Business, Graiingei- Hall, Madison, WI 53706-1323.

Industrial and Labor Relations Review, Vol. 50, No. 2 (January 1997). ? by Cornell Univer-sity. 0019-7939/97/5002 $01.00

237



238 INDUSTRIAL AND LABOR RELATIONS REVIEW

a single individual. This setting is one in which we can carefully test the role of private information in negotiations.

This is the first study we are aware of that empirically investigates what the parties learn from the final offer selection of the arbitrator and the effect this information has on later bargaining behavior. We take as a point of departure theoretical develop- ments that examine negotiating behavior under the threat of interest arbitration and empirical research investigating how arbitrators make decisions. Using data from Wisconsin teacher negotiations from 1977 to 1986, we compare wage outcomes from the final offer arbitration process with the structure of negotiated wage settlements agreed to under the threat of final offer arbitration for those bargaining pairs that receive an award.

Theoretical Framework

In Farber and Katz's (1979) model, the negotiated outcomes the sides prefer to an arbitration award are defined by the parties' risk aversion and by their expectation of what arbitrators will think is the fair outcome. This set of points defines the contract zone and is positive where the parties have identical expectations and both sides are risk-averse. In the absence of "bargaining errors" the parties will reach an agreement that splits this contract zone in order to avoid the costs of arbitration.

Although Farber and Katz do not develop a formal model describing how the parties divide the contract zone', they do show that the mean of the contract zone shifts with changes in the parties' expectations about what an arbitrator will consider a fair settlement. This implies that the weight placed on the facts used by the arbitrator to decide what is fair will be the same as the weight the parties place on these same facts when they reach a negotiated settlement. If these facts are denoted by the matrix X, the two equations describing the fair wage beliefs of arbitrators (Wa) and negotiated settlements (W) are the following:

(1) VV= () + XPl +E(

(2) wV= + X +

If there is no uncertainty about arbitrator preferences (OY , =0), then P() - P( (Crawford 1979). If arbitrator preferences are uncertain, then in a complete information model the negotiated outcome under the threat of arbitration will favor the party that has the lower cost of using arbitration (Babcock 1988). In other words, 3() > PaO if employers have larger average arbitration costs and In, < P( if average union arbitration costs are greater.'

While there is widespread agreement that a complete understanding of interest arbitration must take into account the parties' arbitration expectations, very little is known about the process the parties use to form these expectations. Whereas an analyst may collect historical data on awards and use these data to estimate an arbitrator decision function, negotiating parties nei- ther perform such a statistical analysis nor receive population estimates from on high. Instead, they must observe and learn from the accumulation of experience under the procedure.

We hypothesize two learning mecha- nisms. First, the parties learn from the awards made in other bargaining relationships. In the first nine years of Wisconsin's municipal arbitration law, teachers in over a hundred different school districts used arbitration to establish wages for at least

'Previous research (Anderson 1979; Delaney 1983; Feuille and Delaney 1986; Currie 1989) has failed to find a statistically significantwage difference between parties that arbitrate and those that reach negotiated settlements under the threat of arbitration. These results suggest that average union and employer arbitration costs are equal. This does not mean that arbitration costs are the same for both parties in all bargaining pairs. It is very likely that for particular bargaining pairs, arbitration costs of the parties will be different.

2Gibbons (1988) focused on learning by the arbitrator and developed a model in which the arbitrator learns about the private information of the parties from their final offers.



LEARNING FROM INTEREST ARBITRATION 239

one contract. The written awards in these cases have helped bargaining pairs in districts that have not experienced arbitration to form expectations about the arbitration process. This is evident with respect to wage comparability, which the parties de- fine by comparing their wage to wages in other school districts in the same athletic conference (Olson andJarley 1991). This definition of comparability is widely ac- cepted by the parties and is frequently used as a rationale in the written awards of arbitrators (Halm 1985).

The second learning mechanism, which is the focus of this study, is the learning that occurs when a bargaining pair receives an award. Since the parties to the dispute observe all the "facts" of the case, the arbitration decision provides the parties with new information about the arbitrator's beliefs. Let e ,equal the arbitrator's private information about the case that influences his or her perception of what is a fair settlement and let Z, equal the information considered by the arbitrator and known to the parties directly involved in the dispute (that is, "the facts"). Assuming the arbitrator selects the offer closest to his or her fair wage outcome, the union's (employer's) offer is chosen if Z, + ,, is greater (less) than the mean of the final offers. If ? is normally distributed around Z,, then the expected fair wage belief of the arbitrator for each of the two possible awards is

Ga oWFOU ? WF0B Z1

(3) E(W,,I uwIN(=)=z,+ -y, 2t4(7( W VFOU + WFOB3 Zt

WFoLU+ WF0B Zt

(4) E(Wv,,IUWIN1=O0) =Z- 2,. t1,G( a t

WFOUI+ W4FOB3 Z

UWIN, equals 1 if the union's offer is selected, and otherwise UWIN,= 0; O (.) and 'd (.) are the p.d.f. and c.d.f. for a standard, normal variable; and W and W are the

F)t' F()13

final offers of the union and employer (Johnson and Kotz 1970).

Figure 1 provides a graphical summary of these two equations. When the union's offer is chosen, the parties know the fair wage belief of the arbitrator falls in the shaded area, and the expected fair wage belief is the mean of this truncated distribution (equation 3). When the employer's offer is chosen, the parties know the arbitrator's fair wage belief falls in the un- shaded area, and the mean of this distribution is equal to equation (4). Z,, the first term in equations (3) and (4), is the information known to the parties prior to the decision based on their observation of awards in other bargaining relationships and knowledge of their particular situa- tion. The second term is the private information of the arbitrator that is only revealed to the parties when a final offer selection is made. This term is a non-linear function of the mean offers, Z, and the arbitrator's decision.'

There are two considerations affecting how an award will alter subsequent negotiated settlements. First, if the fair wage belief distribution of arbitrators is station- ary and known by the bargaining pairs, then the final offer award only tells negotia- tors which side received the more favorable draw from the fair wage distribution in that particular round, and this information is of no value in predicting later awards. On the other hand, if 8,at includes a bargaining pair-specific component or a time component unknown by the parties, then the award will provide information about the fair wage

'Learninig by the parties may be easier under conventional arbitration, because the arbitrator may award his or her fair wage outcome. A comparison of negotiator learnin-g under the two arbitration re- gimes is beyond the scope of this study, because our data come entirely from a final offer arbitration re- gime. Equations (3) and (4) describe a rational expectations model of learninig. This model may be cognitively more complex than the process the parties actually use following a decision. This issue is impossible to address in field data. In the empirical specification we do not impose the functional form implied by equations (3) and (4).




E(Fair Wage I Mealn of tile Employer Win) Finial Offers

E(Fair Wage I Union Win)

E(Wa)

Figure 1. Expected Fair Wage Given- FOA Decision.

beliefs of arbitrators that may inform the parties about what an arbitrator would consider appropriate in a later bargaining round. The bargaining-specific component might reflect the arbitrator's judgment about the district's "ability to pay" or wage comparability considerations that are not captured by the observable "facts" of the bargaining relationship. An unobserved time component in the fair wage beliefs of arbitrators implies that these beliefs evolve over time and the parties may learn about the time path of arbitrator beliefs by receiving an arbitration award.

A second factor affecting the impact of an award on later negotiated settlements is the extent of inter-rater reliability among arbitrators in the information revealed by an award and temporal stability in the information revealed by an award. If there is no inter-arbitrator reliability, then the decision process used by the selected arbitrator is independent of the process any other arbitrator would use to settle the dispute. For example, if an arbitrator in a particular case selected a final offer by flipping a coin, the offer chosen would settle the dispute but this outcome would not be useful in predicting the decision of another arbitrator.

There is some experimental evidence showing a high degree of inter-arbitrator reliability. In Dell'Omo (1987, 1989), 22 arbitrators were asked to decide the same set of 34 hypothetical final offer wage dis-

putes. The fact that there were multiple decisions per dispute permits an evalua- tion of inter-arbitrator reliability. If there is no inter-rater reliability in a dispute, then the probability the union's offer is chosen is .5 for each arbitrator. This would be the case if each arbitrator flipped a coin and ignored the facts of the case. Using the binomial distribution for the 22 arbitrators, the .95 confidence interval around a 50/50 split among the arbitrators is approximately 11 ? 4 union victories. In 20 of the 32 cases the share of union offers chosen fell outside this confidence interval, showing some consensus among the arbitrators for some combinations of facts and offers.'

Although the experimental evidence shows a high degree of inter-arbitrator reliability, actual awards may provide less useful information about other arbitrator preferences because of the selection process that determines which cases are arbitrated. The cases in the Dell'Omo experimentwere constructed so there was no correlation between the facts of the dispute and the final offers of the parties (that is, the final offers were held constant). This produced some cases in which the arbitrators dis- agreed very little about which offer was fairer. Whether this level of agreement exists among arbitrators in actual cases depends on the selection process that determines which cases are arbitrated.

Empirical evidence suggesting substantial inter-arbitrator reliability in actual negotiations is provided by the arbitration experience in Iowa (Ashenfelter, Dow, and Gallagher 1985). In the Iowa tri-offer system the parties first present their dispute to

'Farber and Bazerman's (1986) analysis of experimental data showed even greater levels of inter-arbitrator reliability. Assuming 61 awards per scenario, in on-ly 2 of the 25 scenarios did the .95 confiden-ce in-terval for the proportion of employer offers chosen in-clude .5. Inspection of their data by scenario (see their Table 2) shows how "unbalanced" the decisions were across most of the scenarios. It should be noted, however, that usinlg these same data, Bazerman (1985) found the weights placed on the facts of the case differed across arbitrators.




a factfinder for a non-binding recommendation. If this recommendation does not produce a settlement, each side submits a final offer to an arbitrator, who then selects one of the final offers of the parties or the factfinder's recommendation. While factfinders and arbitrators are drawn from the same neutral panel, in each contract dispute different individuals are assigned to the two roles. In this system, Ashenfelter et al. estimated a correlation of .8 between the error terms describing arbitrator and factfinder beliefs. Despite this large correlation, approximately 40% of the parties fail to settle after the factfinder's report and eventually receive an award. This .8 correlation is substantially greater than what we expect in the present study, where the correlation is between arbitrator beliefs in different bargaining rounds separated by at least a year. Nevertheless, this evidence suggests there is sufficient inter-arbitrator reliability in actual arbitration cases to inform the parties about what would be considered fair in the next bargaining round.

Awards will alter subsequent negotiations when there is both inter-arbitrator reliability and temporal stability in the private information collected by arbitrators. If these conditions exist, an award will have two related effects on subsequent negotiations. First, the award tells the parties where the arbitrator's fair wage belief falls relative to the mean of the parties' final offers. Thus, settlements in negotiations subsequent to an award will be higher if the union's offer is chosen than if the employer's offer is selected. Second, know- ing where the arbitrator's beliefs lie relative to the mean of the final offers also reduces the parties' uncertainty about what will be perceived by arbitrators as fair in the next bargaining round. Since this reduc- tion in uncertainty narrows the contract zone or the range of negotiated settlements each side would prefer in lieu of arbitration, the dispersion of settlements will also decline after arbitration is used.5

5This assumes n-egotiated settlements fall within- the entire ran-ge defined by the contract zone and do

Sample and Data Description

To evaluate the impact of an award on negotiating behavior, we employ a standard "pre-treatment/post-treatment" de- sign in which the "treatment" variable is the final offer selection of the arbitrator.6 The study uses data on negotiated wage settlements in the bargaining rounds before (t - 1) and after (t + 1) the bargaining round in which a wage dispute was settled by a final offer decision, where t indexes a school year. The sample of awards comes from Wisconsin teacher and school board negotiations during the first nine years of the state's final offer law covering local government negotiations outside of pro- tective services.7 265 final offer wage decisions were made between teachers and k-12 school districts in the first nine years of the Act.8 From these awards a balanced panel of 152 bargaining pairs was constructed in the following steps.'

First, the bargaining pairs for the 265 final offer decisions were matched with the wage outcomes in the rounds immediately preceding and following the award. If the wage outcomes in the preceding and following rounds were both a result of negotiated settlements, the observation was in-

not simply equal, for example, the center of the contract zone. If settlements were always equal to a single value, the variance in settlements would not decline as the size of the contract zone shrank.

'The "treatment" is not whether the parties uise arbitration, but, where arbitration is used, how settle- me nts change based on the final offer selection of the arbitrator.

7See Olson and Jarley (1991) and Babcock and Olson (1992) for a more complete description of the law and the data, and a description of the steps in Wisconsin's final offer procedure. Note, however, that a key feature of the procedure is that the parties observe the final offer of their opponent and set their final offer- with full knowledge of their oppon-en-t's position.

'The sample used in this study is smaller than Olson and jarley's (1991) sample because they also included awards made in k-8 districts and 9-12 districts.

'>The balanced sample was created to simplify the empirical analysis.




Table 1. Summary of Sample Frequencies by School Year.

Year of Arbitration No. of No. oft-i No. of t+1 No. oft-i and Decision (t) Awavards Settlements Settlements t+J Settlements

1977-78 4 4 -

1978-79 12 9 12 1979-80 11 11 9 9 1980-81 27 24 22 21 1981-82 31 27 27 23 1982-83 68 62 65 60 1983-84 19 18 14 13 1984-85 36 33 29 26 1985-86 57 49 Total 265 233 182 152

Source: Authors' calculations; see text.

cluded in the analysis. The observation was deleted if the wage was set by arbitration in either round t - 1 or round t + 1. Second, we eliminated the observation if the negotiated settlement in either round t - 1 or round t + 1 was "sandwiched" between two final offer decisions. We did so because such a negotiated settlement is both the t- 1 settlement for a later award and the t + 1 settlement for first award. Third, since the law did not go into effect until the middle of the 1977-78 school year, we assumed negotiations carried out under the threat of arbitration occurred for the first time for contracts that became effective with the 1978-79 school year. This eliminated awards for the 1977-78 and 1978-79 school years. Similarly, awards for the 1985-86 school year were eliminated because t + 1 settlement data were not available. 113 of the 265 awards were eliminated from the sample, leaving 152 usable pairs. Seventy- three of these awards were eliminated because they occurred either in 1985-86 or prior to 1979-80. Finally, 40 awards were eliminated because there were awards in two consecutive contracts or because only one negotiated contract occurred between two final offer decisions. Table 1 summa- rizes the results of this sample selection process by school year.

In interpreting the results of this study, the endogenous nature of the sample selection process must be recognized. Since the

sample was defined by the decision of the parties to arbitrate, an effect on negotiated settlements following arbitration could be attributed to learning from the process of arbitration, learning from negotiated settlements of other parties, or an inherent difference between parties that arbitrate and those that do not. While we address the first two alternatives, a fuller treatment might address the third as well. Unfortu- nately, which parties arbitrate and how they differ from parties that negotiate have been difficult questions for researchers to an- swer, and they are beyond the scope of this study.

The dependent variable in the wage regressions and the final offers is measured using the percentage wage increase for a teacher with a Master's degree who is paid the maximum salary permitted by the salary schedule. Thus, A W4 l is the percentage change in the Master's degree maximum point on the salary schedule from school year t - 2 to t - 1. We also assumed the parties form their arbitration expectations in t - 1 and t + 1 using information on five exogenous variables: changes in the cost of living during the first year of the contract; changes in local private sector wages during the first year of the contract; the local property tax rate in the year preceding the first year of the contract; property wealth per student for the first year of the contract; and the district's wage level relative




Table 2. Sample Means and Standard Deviations. (n = 152)

Variable Period t-1 Period t Period t+1

Salary Increase, M.A. Maximum (%) 8.344 7.331 7.127 (3.379) (2.498) (2.191)

Taxes -.200 -.203 -.194 (.718) (.808) (.804)

Wealth .016 -.036 -.033 (.812) (.715) (.706)

Inflation (%) 7.076 4.841 3.540 (3.725) (3.347) (1.835)

Private Sector Wage Increases 7.868 5.601 5.796 (4.620) (6.007) (4.703)

Relative Wage Level 99.440 99.989 99.570 (5.550) (5.360) (4.690)

Aver-age Incr-eases in the Athletic Coniferenice 7.629 (2.125)

UWIN (Equal 1 if Union Wins in Time t) .533 DIFFI (W - W ) if UWIN = 1 1.437

(2.219) DIFF2( -W if UWIN = 0 -1.357

(2.219) Mean of the Parties' Final Offers 7.318

(2.096)

SoIl7ce: Authors' calculationis; see text.

to the average wage level in the athletic conference for the year preceding the first year of the contract."' The tax rate and property wealth measures were standard- ized relative to all districts in the state for the year. The relative wage measure equals 100 if the district's wage level was equal to the athletic conference mean in the preceding year. The tax rate measure is equal to zero if the district's tax rate was equal to the state average in the preceding year. Table 2 reports the descriptive statistics for the variables.

A Comparison of Wage Changes Before and After Arbitration

In this section we investigate whether or not the final offer award in round t alters

"'Most of these five variables have been used in previous r-esear-ch on arbitr-ator decision-makinig (Olson andJarley 1991).

negotiated settlements in round t + 1 by comparing negotiated outcomes in t - 1 and t + 1. The percentage wage changes in these two rounds are hypothesized to be a linear function of the five exogenous variables and an error term with two components:

(5) AW,l = Jk.Il + X. , + v.+ u

(6) AW,+ = , + X.,+I,+ + v. + U

The error term is assumed to have a bargaining-specific fixed component (vi) and a normally distributed error term indepen- dently distributed over time and across bargaining pairs (uit,) . Vi, captures either constant, unobserved (to the researcher) fac- tors used by arbitrators and known to the parties or stable differences across bargaining pairs in the relative costs of using arbitration.

The following two hypotheses test whether the arbitration experience




changed the structure of negotiated wages:

HI: Vl = V+

H2: Var(vi + u,,l) = Var(vi + u,+ )

Rejection of H shows that the weight placed on the observable facts of the case is altered by the arbitration experience. H.2 tests whether or not arbitration narrows the "bargaining range" in later negotiations by re- ducing the parties' uncertainty about the arbitration process and, therefore, the variance in settlements.

The wage change equations are estimated using two different specifications. Equa- tions (5) and (6) are jointly estimated by maximizing the log of the likelihood function for f( W, W 1 ),where the error terms are assumed to be bivariate normal and independent of the exogenous variables. In the second specification we control for the unmeasured fixed effect (v ) using the following first difference specification on all the variables:

(7) AW V AWVl (I+ -

+ X- + Ul.+1 - 1

Although less efficient than the MLE "random effects" model, equation (7) gives unbiased estimates when v. is correlated with the exogenous variables. A weakness of the first difference specification is that it does not permit a test of H2 with only two periods of data.

Table 2 shows that the unconditional standard deviation in wages declined substantially after arbitration, from SD(VX'l) = 3.38 to SD(W1+,) = 2.19. The difference in wage variability between the two periods declines only slightly after conditioning on the exogenous variables. The random effect estimates reported in Table 3 show that the equation standard error declined by about one-third after arbitration, from about 2.99 to 2.05." The hypothesis that

"Not surprisingly, the estimated error standard deviations from the OLS estimates are very similar; they are 3.05 for the AW-, equatioin and 2.08 for the AW,+, equation.

the error variances for the two equations are equal is easily rejected (p < .0001). This finding suggests that arbitration reduces the parties' uncertainty about the arbitration process and narrows the contract zone that defines the range of negotiated settlements the parties prefer to an arbitration award.

Table 3 reports the random and fixed effect specifications for AW, l and A,+,1.'2 In the bargaining round preceding arbitration, both specifications show that wage changes are positively related to property values per student (wealth) and private sector wage increases in the county, and negatively related to the district's pay level relative to other districts in its athletic conference.

A comparison of column (1) with (3) and column (2) with (4) in Table 3 shows that the random and fixed effect estimates are different for several of the variables. For example, the fixed effect wealth coefficient is substantially larger than the random effect estimate in round t - 1, and the difference between the estimated wealth effects is even more dramatic for round t + 1. These comparisons suggest the random effect estimates are not unbiased, because the error term, vi, is correlated with exogenous variables. This conclusion is supported by a Hausman (1978) test, which marginally rejects the random effects specification in favor of the fixed effects model (X2df = 15.785, p = .0715). Because of the result from this test, we perform the remaining analysis using the fixed effect model.

1'2In the usual two-period fixed effect model, the parameters are assumed to be the same across the two time periods, and the parameters are equal to the OLS estimates of the change in the dependent variable over the two periods regressed on the difference between the variables calculated over the two periods. While equation (7) does not impose this con- straint, to test H, we estimate the model with constant PIs.




Table 3. Random and Fixed Effect Parameter Estimates for Wage Changes for Rounds t-I and t+1.

(Standard Errors in Parentheses)

Random Effect Fixed Efiffect

Variable W W

Constaint 24.307*** 17.168*** (4.548) (4.585)

Taxes -.335 -.167 -.811 -.830 (.394) (.345) (.721) (.660)

Wealth 1.167*** -.155 2.865*** 2.411 ** (.226) (.383) (.900) (1.078)

Inflation- -.064 .288** -.199** .204** (.079) (.163) (.098) (.191)

Private Sector Wage Increase .140** -.023 .177*** -.019 (.063) (.046) (.066) (.070)

Relative Wage Level -.168*** -.110** -.656*** -.673*** (.043) (.046) (.113) (.114)

Sigma 2.988*** 2.048*** 3.546 (.156) (.098)

Log L -702.57 R 2 .439

Note: In the fixed effect model for t-1, the coefficients are on1 -1 times each of the variables. Source: Authors' calculations. **Statistically significant at the .05 level; ***at the .01 level (onie-tailed tests).

Four variables constructed from the final wage offers of the parties and the arbitrator's selection are added to equation (7) to investigate how features of the award in round t might account for the differences in the structure of wage changes before and after an award. The revised equation (7) is

(8) AWV '+-AWVV, '+= - " ' + X. -X + O UWIN

+C2((W + W )/2) + (X3DIFF1

+ (X4DIFF2 + Ui+-Ui,.-

UWIN, is a dummy variable equal to one if the union's final offer is chosen. The parameter on this variable measures the shift in settlements in round t + 1 based on the arbitrator's decision. This is a key variable in the analysis because the FOA selection tells the parties whether the fair wage belief of the arbitrator is above or below the mean offer (see equations 3 and 4). If the information gained from an award helps the

parties decide what is considered fair in round t + 1, higher settlements are predicted when the union wins. Holding the mean of the final offers constant, we expect the coefficient on UWIN, to be positive.

In final offer arbitration the award does not correspond to the fair wage belief of the arbitrator but, rather, to the final offer closest to this belief. Therefor-e the settlement the parties negotiate in t + 1 may be affected by the difference between the parties' final offers in period t.'3 If the parties are risk-neutral, then the difference between the offers is positively correlated with the parties' uncertainty about the fair wage beliefs of the arbitrator.14 In addition, the

3The following predictions were suggested to the authors by Robert Gibbons.

4The difference between the final offers in the risk neutral case is equal to G/0(0), where 0(.) is the p.d.f. for a standard normal variable.




7'able 4. Fixed Effect Estimates of Negotiated Wage Changes for Rounds t-1 and t+ 1.

(Dependent Variable = WV ,+, - VV,,; Standard Errors in Parentheses)

Variable (a) (b) (C)

Constant 14.914*** 14.426*** 15.015*** (6.000) (5.958) (5.981)

-(Taxes,-,) -1.137 -.855 -.790 (.693) (.682) (.684)

-(Wealth,-,) 2.477*** 2.440*** 2.722 (.876) (.870) (.857)

-(Inflation,1) -.075 -.076 -. 182** (.114) (.114) (.093)

-(Private Sector .174*** .176*** .159** Wage Increase,) (.064) (.064) (.063) -(Relative Wage -.879*** -.868*** -.806*** Level,) (.125) (.123) (.117)

Taxes,+, -1.146** -.908 -.867 (.635) (.682) (.629)

Wealth,+, 2.351** 2.193** 2.482*** (1.047) (1.034) (1.024)

Inflation,+, .227 .221 .127 (.190) (.190) (.182)

Private Sector -.041 -.028 -.014 Wage Increase,+, (.068) (.067) (.067) Relative Wage -1.066*** -1.054*** -.982*** Level,+, (.139) (.139) (.132) UWIN 1.349** 2.300*** 2.029***

(.994) (.637) (.619) DIFFI I ( W- wF-B .027 if UWIN = 1 (.234) DIFF2, ( W -VW'') 333** if UWIN = 0 (.171) Mean of the Parties' .364 .291 Final Offers (.183) (.180) Sigma 3.325 3.347 3.366 R2 .489 .474 .465

Source: Authors' calculations. **Statistically significant at the .05 level; ***at the

.01 level (one-tail tests).

revision in the parties' belief about what the arbitrator thinks is fair is also a positive function of the parties' uncertainty about the arbitrator. This can be seen from equations (3) and (4); as c5,,, increases, the revision in the parties' expectations about Wa also increases. This implies that when the difference between the awards is "large,"

there is greater adjustment in t + 1 settlements because the parties learn more from the award relative to disputes in which there is less uncertainty and the offers are closer together. The following two variables capture this effect:

DIFFI = W - W if UWIN = 1, otherwise DIFFI = 0,

DIFF2 = W - W if UwIN = O, otherwise DIFF2 = 0.

Each of these variables is predicted to have a positive coefficient.

The third variable added to the model is the mean of the parties' final offers. This is included to capture temporal changes affecting the union, board, and arbitrator beliefs about what is fair that are not captured by the observed variables.'5

Column 1 of Table 4 reports the estimates for equation (8). The results show that the arbitration award alters the bargaining behavior of the parties. The coefficient on UWIN, is significant at the .05 level (one-tail) and suggests negotiated settlements are 1.3 percentage points higher when the union's offer is chosen in round t than when the school board's offer is selected. The mean of the parties' offers in round t is also positively related to the change in settlements from t - 1 to t + 1. Since the arbitration process occurred be-

'5The interpr-etation of the parameters on the four- arbitratioin variables in the first differ-ence specification of equation (8) requires a brief explanationi. Because the values of these var-iables do not change over the two rounds, their- separate effects on AW,Yl and A W,+, are not identified. Instead, these variables measure the difference between the effect of arbitration in rounid t on wage increases in the two rounds (that is, , - t ,) . If arbitration in round t has the same effect in negotiated settlements in t - 1 and t + 1, the coefficients on the four arbitrationi variables will be zero. Since these variables are constructed from events that occurred after round t - 1, we hypothesize that the effects of these var-iables will be differenit between the two time periods and the parameter estimates r-eflect the impact of arbitration on wage changes in the rounid following the award.




tween the two bargaining rounds, we suspect this variable is picking up a time trend in the parties' (the union's, employer's, and arbitrators') beliefs that is not captured by the other variables in the model.

The coefficients on DIFFI and DIFF2 are positive, and the effect of DIFF2 is both statistically significant at the .05 level and substantial in practical terms. These positive coefficients mean the wage differential between a union victory and an employer victory, holding the mean final offers constant, is positively related to the difference between the final offers of the parties. Win- ning with a more extreme final offer has a greater impact on later negotiated settlements than winning with a less extreme final offer, because more extreme final offers imply greater uncertainty about the arbitrator's beliefs and, therefore, a larger revision in arbitration expectations following an award.

Estimates that exclude DIFFI and DIFF2

are reported in column 2 of Table 4. The estimated effect of a union victory increases and the standard error declines by about a third because of the positive effects of DIFFI and DIFF2 and their correlations with UWINt

(by construction). Compared to a settlement following an employer arbitration victory, a union arbitration victory in round t

causes negotiated wage increases to be 2.3 percentage points greater in round t+ 1. As the last column shows, this effect declines slightly to 2 percentage points when the mean of the final offers is omitted from the model. This impact is very substantial compared to the average wage increase across the two bargaining rounds of 7.74%.

Above, we hypothesized that the information the parties learn from an award that would be useful in later negotiations could reflect either pair-specific information considered by the arbitrator that the parties do not directly observe or information about the evolution of arbitrator beliefs over time that is only observed when awards are made. It is possible to decompose the estimated effect of the award on settlements into these two components by adding a set of time dummies to the negotiated wage change regressions. If the addition of the time

dummies changes the coefficient on UWIN, then there is a correlation between negotiated changes and the fraction of cases decided for the union in period t - 1. We interpret the effect of this correlation on the change in the coefficient on UWIN to be an estimate of what is learned from the final offer selection about the evolution of arbitrator beliefs. When yearly time dummies are added to the equation as shown in the last two columns of Table 4, the estimated effect of UWIN iS 1.137 (SE = .489) for the specification in column (b) and .862 (SE = .481) for the column (c) specification. Each of these coefficients remains statistically significant at the .05 level (one- tail test). These estimates suggest that 50- 58% of the impact of the final offer award on negotiated settlements is explained by what the parties learned about the evolution of arbitrator beliefs over time. The remaining effect is pair-specific information about the fair wage beliefs of arbitrators.

Does the arbitration experience change the weight the parties place on different variables when they negotiate a settlement? Thejoint hypothesis that P3_, = - for taxes, wealth, inflation, private sector wage increases, and relative wage levels is strongly rejected by the data (F(5 1i9)=3.33, p = .007). The reasons for this result are shown in Table 5, where the differences between the estimated parameters across the two rounds are reported. Following arbitration, the parties give greater positive weight to inflation, compress wage levels by agreeing to larger wage increases in districts with lower relative wages, and give less weight to private sector wage increases.

The Structure of Negotiated and Arbitrated Wages

The effect of the final offer selection of the arbitrator on the change in negotiated wages between round t - 1 and round t + 1 suggests that when the parties receive an award they modify their beliefs about the decision process of arbitrators, and this changes the average bargaining outcome in round t + 1. A companion question




Table 5. Differences Between the Fixed Effect Parameters for P, and f+.


Variable V] -

Taxes -.053 (.523)

Wealth .247 (.574)

Inflation -.296** (.215)

Private Sector Wage Increases .204*** (.099)

Relative Wage Levels .187*** (.068)

Source: These differences were calculated from Columni (b) of Table 4. The standard errors were calculated from the parameter variance-covar-iance matrix.

**Statistically significant at the .05 level; ***at the .01 level (one-tail tests).

raised by these results is whether the structure of negotiated wages fits the structure of arbitrator beliefs about fair wage settlements. Although we found from the results in Table 4 that the arbitration process modi- fies the wage structure, we have not cross- checked the negotiated wage structure with arbitrator beliefs. If the parties learn from the arbitration experience, then t+ 1 settlements may more closely coincide with the fair wage beliefs of arbitrators than settlements in round t - 1. We investigate this question by comparing estimates of the fair wage beliefs of arbitrators with negotiated wages in the two rounds.

We first test whether the parameter weights are the same for negotiated wage increases and arbitrator beliefs by comparing the following two wage equations with estimates of the fair wage beliefs of arbitrators derived from the final offer decisions:

(9) AWU,> = + Xi. + V. + u -1

(10) AWVV+, = + X1.,, + V. + u

The first two columns of Table 6 report

the OLS estimates of equations (9) and (10). Columns (3) and (4) of Table 6 report the differences between the OLS coefficients and the beliefs of arbitrators using a model of arbitrator fair wage beliefs that is a function of taxes, wealth, inflation, relative wage level, mean negotiated athletic conference wage increase, and the mean private sector wage increase in the county. Each wage equation is jointly estimated with the arbitrator decision equation, and the standard errors for the difference in the coefficients are calculated using the estimated parameter variance-cova- riance matrix. In round t - 1 the weight placed on two of the five exogenous variables (for example, wealth and inflation) by the parties is significantly different (p < .10) from the arbitrator weight. On the other hand, none of the differences between the arbitrators' weights and the parties' weights on the facts in round t + 1 are statistically significant. The table shows the standard errors are very similar in columns (3) and (4), and the point estimates for the weight placed on the facts of the case more closely conform to the beliefs of arbitrators in round t + 1 than in round t- 1. These results suggest that the structure of negotiated settlements among those who use arbitration con- verges toward a structure consistent with the beliefs of arbitrators after a final offer award is received.

Comparisons with a "Control" Group

A plausible alternative explanation for our finding of a significant effect of an award on negotiated settlements is that the learning that occurs in our sample between t- 1 and t + 1 is based on the arbitration experience of other bargaining pairs. As we noted in the introduction, we do believe this is also an important means by which the parties learn about what to expect in arbitration. The issue is whether or not this form of learning accounts for the "learning by doing" effect we identify in this study.

It is possible to test between these two alternative explanations by observing the bargaining behavior for districts that never




Table 6. OLS Estimates for the Change in W,4,, the Change in WV and Their Differences with Arbitrator Beliefs.


OLS Estimates

Variable WI W I)

Constant 24.258*** 20.040*** 10.507 -6.289 (4.612) (3.664) (12.432) (10.928)

Taxes -.433 -.194 .443 .204 (.369) (.232) (.777) (.674)

Wealth 1.176*** .042 -1.863*** -.728 (.321) (.266) (.853) (.970)

Inflation -.087 .257*** .601*** .257 (.068) (.100) (.212) (.253)

Private Sector Wage .164*** -.009 .024 .197 Increase (.054) (.039) (.159) (.136) Relative Wage Level -.168*** -.141*** .072 .046

(.045) (.036) (.124) (.109) Sigma 3.045 2.076 R 2 .215 .159

Soutrce: Authors' calculations. ***Statistically significant at the .01 level (one-tail test).

used arbitration during the study period.' If results in these districts are similar to the results reported above, then our estimates of learning are suspect, because the school districts in the control sample can only learn about arbitration from other bargaining pairs. Eighty k-12 school districts that never experienced the arbitration process through the 1985-86 school year are used as a control group. For these districts, a random bargaining round from 1979-80 through 1984-85 was selected to correspond to time period t. Data from bargaining round t - 1 and t + 1 are then used to examine the changes in the variance and structure of negotiated wage changes. While this control group is far from ideal because districts that have never arbitrated presum- ably differ in unobservable ways from dis-

'6The control group includes districts that never initiated or received a final offer award. In some districts the parties began the arbitration process by agreeing to a set of final offers but then settled before a final offer selection was made. These districts are excluded from the control group.

tricts that have arbitrated, this sample does provide some evidence on whether or not the earlier results are simply due to greater general knowledge about arbitrators caused by greater statewide experience with the law.

The observed decline in the standard deviation in negotiated wage increases reported in Tables 2 and 3 is not due to a general decline in the variance of negotiated wage increases. In the control group, the unconditional standard deviation in negotiated wages increased from 4.1% in period t- I to 4.5% in period t + 1. Condi- tioning on the five exogenous variables using OLS, the equation standard error is 3.9 in t- l and 4.1 in t + 1. This result is very different from the results obtained for those pairs that arbitrated in period t and is con- firming evidence that the use of arbitration did reduce the dispersion in post-award settlements.

We also estimate equation (7) for the control group to test whether there is any significant change in the weight placed on the five exogenous variables between periods t- 1 and t + 1. Table 5 shows there is a




significant change between these two periods for those pairs that arbitrated in period t. Different results are obtained for the control group. The joint test that the weights placed on taxes, property wealth, relative wage levels, inflation, and private sector wage increases are the same in the two periods could not be rejected (F569 = 1.06, p = .39). This result provides further evidence that the changes in the wage structure that occurred for those parties that received an award were caused by their use of arbitration.

Conclusions

Our findings show that the parties' expectations about outcomes from arbitration are shaped by their own experience with the procedure. While the parties un- doubtedly learn by observing the arbitration outcomes in other bargaining pairs, additional information about the arbitration process is gained by receiving a final offer award. The evidence we obtain by comparing negotiated settlements in the round before arbitration with the settlements in the round after arbitration, using data on Wisconsin teacher negotiations from 1977 through 1986, demonstrates that the bargaining behavior of the parties is directly affected by the arbitration

experience. This evidence takes three forms.

First, compared to settlements in the round prior to arbitration, the variance in negotiated settlements declines in the round after an award by about 30%. This result supports the hypothesis that a final offer selection narrows the contract zone in later bargaining rounds because it reduces the parties' uncertainty about the arbitrator's beliefs in the next bargaining round. Second, the negotiated wage structure is statistically different from the wage structure based on the arbitrator's beliefs in the round prior to arbitration, but not in the round after arbitration, suggesting that the parties learn about the weights arbitrators place on the facts of the dispute from the award. Finally, the patterns of negotiated settlements differ between pairs that use arbitration and pairs that have never used the procedure.

These results are broadly consistent with models such as those developed by Farber and Katz (1979) and Gibbons (1988), in which bargaining behavior is shaped by the parties' expectations about the behavior of the arbitrator. An award gives the parties improved common understanding of arbitrator preferences and thereby helps them achieve negotiated settlements in later bargaining.

REFERENCES

Anderson, John C. 1981. "The Impact of Arbitra- tion." Industrial Relations, Vol. 20 (Spring), pp. 129- 48.

Ashenfelter, Orleyjames Dow, and Daniel Gallagher. 1985. "Arbitrator and Negotiation Behavior Under an Appellate System." Unpublished paper, Princeton University.

Babcock, Linda C. 1988. "Negotiation Under the Threat of Final Offer Arbitration: A Theoretical and Empirical Analysis." Diss., Departmen t of Eco- nomics, University of Wisconsin.

Babcock, Linda C., and Craig A. Olson. 1992. "An Analysis of the Causes of Impasse in Labor Dis- putes. " Industrial Relations, Vol. 31, No. 2 (Spring), pp. 348-60.

Bazerman, Max H. 1985. "Norms of Distributive Justice in Interest Arbitration." Industrial and Labor Relations Review, Vol. 38, No. 4 Uuly), pp. 558-70.

Crawford, Vincent P. 1979. "On Compulsory-Arbitra- tion Schemes." Journal of Political Economy, Vol. 87, No. 1 (February), pp. 131-60.

Currie, Janet. 1989. "Who Uses Interest Arbitration: The Case of British Columbia's Teachers, 1947- 198 1. " Industrial and Labor Relations Review, Vol. 33, No. 1 (October), pp. 363-79.

Delaney, John Thomas. 1983. "Strikes, Arbitration, and Teacher Salaries." Industriial and LaborRelations Reviezv, Vol. 36, No. 3 (April), pp. 431-46.

Dell'Omo, Gregg G. 1987. "Arbitration Application of Wage Criteria Under the Wisconsin Police and Firefighter Arbitration Act: An Empirical Analysis." Diss., University of Wisconsin.

1989. "Wage Disputes in Interest Arbitration: Arbitrators Weigh the Criteria." Arbitrator Journal, Vol. 44 (June), pp. 4-13.

Farber, Henry S., and Max H. Bazerman. 1986. "The




General Basis of Arbitrator Behavior: An Empirical Analysis of Conventional and Final-Offer Arbitra- tion." Econometrica, Vol. 54, No. 6 (November), pp. 1503-28.

Farber, Henry S., and Harry C. Katz. 1979. "Interest Arbitration, Outcomes, and the Incen-tive to Bar- gain." Industrial and Labor Relations Review, Vol. 33, No. 1 (October), pp. 55-63.

Feuille, Peter, and John Thomas Delaney. 1986. "Collective Bargaining, Interest Arbitration, and Police Salaries." Industrial and Labor Relations Re- view, Vol. 39, No. 2 (January), pp. 228-40.

Gibbons, Robert. 1988. "Learning in Equilibrium Models of Arbitration." American Economic Review,

Vol. 78, No. 5 (December), pp. 896-912. Halmn, Francis P. 1985. "Athletic Conference: The Question of Comparability." Unpublished paper, Wisconsin Public Employer Relations Association.

Hausman, Jerry A. 1978. "Specification Tests in Econometrics." Econometrica, Vol. 46, No. 6 (No- vember), pp. 1251-72.

Johnson, N. L., and S. Kotz. 1970. Distributions in Statistics: Continuous Univariate Distributions. New York: John Wiley & Sons.

Olson, Craig A., and PaulJarley. 1991. "Arbitrator Decisions in Wisconsin Teacher Wage Disputes." Industrial and Labor Relations Review, Vol. 44, No. 3 (April), pp. 536-47.



Documents

Learning from Interest Arbitration: The Next Round