Data and empirical results

the desire to index is strong enough to result in an indexation clause; however, the Ž . desire to index, which is what is on the left hand side of Eq. 3 , is unobservable. U Ž . Substituting the reduced form equation for COLA s X Ł q Õ on the left 3 3 Ž . hand side of Eq. 3 , yields: X P q Õ s g DUR q g DWAGE q X b q u . 3 X Ž . 3 3 31 32 3 3 3 Solving for the observable DUR results in: ˆ ˆ DUR s 1rg X P y g rg X P y 1rg X b Ž . Ž . Ž . 31 3 32 31 2 31 3 3 ˆ ˆ q Õ y g rg X P I P y 1rg X P I P Ž . Ž . Ž . Ž . 1 32 31 2 2 31 3 3 ˆ Y s XQl q w 3 Ž . 3 where ˆ ˆ ˆ Q s P , IP , yJ ; 3 2 3 w J is a K = K matrix of zeroes and ones such that XJ s X ; and l s 1rg , 3 3 3 3 31 Ž . x X g rg , 1rg b . 32 31 31 3 Ž . Amemiya shows that the Heckman estimator of l via least squares is: y1 X X X X ˆ ˆ ˆ ˆ l s Q X XQ Q X DUR. 9 Ž . Ž . ˆ The parameter estimates of interest — g ,g , b — can easily be identified from ˆ ˆ 31 32 3 ˆ Ž . l. The variance–covariance matrix for g , g , b can also be estimated using 31 32 3 ˆ the variance–covariance matrix of l. As was true of the parameter estimates for DUR and DWAGE, Amemiya’s paper proposes a more efficient GLS estimate for the parameter vector correspond- ˆ ˆ ˆ w x ing to the latent variable. This is obtained by forming G s P ,P ,J and then 1 2 3 Ž Ž .. calculating the estimate of the parameter vector a s g , g , b such that: 3 31 32 3 y1 y1 y1 X X G ˆ ˆ ˆ ˆ a s G Var h G G Var h P 10 Ž . Ž . Ž . ˆ ˆ ˆ ž 3 3 3 3 where h is a disturbance term.The variance–covariance matrix of a G is ˆ 3 3 obtained by taking: y1 y1 X G ˆ ˆ Var a s G Var h G . 11 Ž . Ž . ˆ ˆ Ž . ž 3 3

5. Data and empirical results

Ž . Ž . The contract data used in estimating Eqs. 1 – 3 were drawn from Current Ž . Wage DeÕelopments CWD , published by the Bureau of Labor Statistics. The sample consists of 1876 contracts negotiated between 1977 and 1988 covering Ž . firm-union bargaining pairs in a variety of industries spanning all broad 1-digit sectors of the economy. Mean contract length during the sample period is 29.5 months. The standard deviation and the range of the data are 9.4 months and 4.6 years, respectively. 5.1. Uncertainty measures Since the focus of this paper is on the effect of uncertainty on contract duration, it is worth discussing the definitions of the uncertainty variables in some detail at the very outset. In his theoretical work, Danziger showed that three types of uncertainty should be important in determining contract length: nominal uncer- tainty, relative uncertainty, and real uncertainty. The empirical question is how to measure each concept. Nominal uncertainty is the easiest to measure in the sense that previous contract duration studies employ measures of this type of uncertainty in their analyses. The variable measuring nominal uncertainty in the empirical work below is entitled INFUNCRT. It was constructed using the sliding regression technique advocated by Christofides and by Christofides and Wilton. Specifically, the inflation rate was regressed against past values of itself in an 11-lag, third-degree polynomial. The sample period begins in the third quarter of 1959 and extends to the quarter prior to signing of a given contract. Thus 44 regressions were run in all. The inflation Ž . data specifically, the percent change in the GNP deflator were drawn from the CITIBASE database. The nominal uncertainty measure is the mean square error of the regression pertaining to the relevant year and quarter prior to signing of the contract of interest. 12 This method presumes that agents are able to forecast inflation on the basis of the past behavior of inflation and that they have no more information available to them than is available at the time of the contract negotiations. In his QJE paper, Danziger also argued that ‘‘relative’’ uncertainty would be inversely related to contract length. In this regard, he was referring to uncertainty Ž . of consumer prices i.e., prices that matter to consumers vis-a-vis producer prices Ž . i.e., prices that matter to firms . The variable used in the empirical work to measure this aspect of uncertainty is RELUNCRT. It is constructed in a fashion similar to INFUNCRT using the sliding regression technique. Specifically, the ratio of the consumer price index to the producer price index was regressed against past values of this ratio using an 11-lag, third degree polynomial. 13 The mean 12 In other words, if the contract of interest was signed in June of 1985, then the mean square error of the regression spanning the period 59III–85I was used as the measure of nominal uncertainty. 13 Ž . This functional form was arrived at by using the entire sample period 1950 to 1987 to experiment with a variety of functional forms. The 11-lag, third-degree polynomial yielded the best fit. square error of this regression up to the quarter before the signing of the contract was used as the uncertainty measure. The measure of chief interest to this study is that which proxies for what Danziger referred to as real uncertainty. The literature is not very specific about exactly what constitutes a real shock. Real shocks may be due to an unexpected Ž . price change for some crucial input in the production process e.g., oil . A real shock may occur because of an unexpected change in productivity or technology. Ž Or such a shock may occur because of a change in preferences say, consumer . demand or labor supply . All of these factors are difficult to measure, but changes in such factors should affect the aggregate unemployment rate. In order to measure real uncertainty, therefore, I applied the sliding regression technique to the aggregate unemployment rate. Specifically, the following regression was fit for the quarterly aggregate unemployment rate: u s d q b u q g p q 1 y u B y u B 2 ´ 12 Ž . Ž . Ý Ý t i tyi i tyi 1 2 t i i where u is the aggregate unemployment rate at time t; p is the rate of inflation; t and B is the backward shift operator. After some experimentation, it was determined that the lagged unemployment rate terms were best treated as an 11-lag, third-degree polynomial, while the lagged inflation terms were best treated as an 11-lag, second degree polynomial. Lagged inflation is included in the regression in order to purge the effect of excess demand from the unemployment rate. The unemployment rate data commence in 1960 and a regression was run from 1960 to the quarter in which the contract of interest was signed. The real uncertainty measure is the mean square error of this regression and is referred to as URUNCERT in the work below. This measure of real uncertainty is related to changes in the unemployment rate that can neither be predicted from past movements in the rate of inflation nor from past movements in the rate of unemployment. By allowing for the rate of inflation Ž in the regression, changes in unemployment due to nominal factors such as . changes in the money supply or changes in fiscal policy are accounted for. As an additional control for real uncertainty, I also created a variable measuring Ž . real uncertainty within the local labor market RLURSDLG . In order to generate this variable, state unemployment was first predicted by regressing the state unemployment rate against the lagged state unemployment rate, against the national and the lagged national unemployment rate, and against a cubic function of time. The time period for the regression is 1960 to the year prior to the contract Ž . thus, the presumption is that agents only have information to the present . RLURSDLG was then generated by taking the actual state unemployment rate minus the predicted state unemployment rate in the year prior to the signing of the contract and dividing through by the actual state unemployment rate. Positive values of the variable indicate a surprisingly bad year while negative values are indicative of a surprisingly good year. 5.2. Additional exogenous Õariables A number of other variables were used as proxies for the factors sketched as determinants of DUR, DWAGE, and COLA U in Section 3. Table 1 provides definitions and summary statistics, indicates whether a given variable was included Ž . Ž . in the X matrices of Eqs. 1 – 3 , and indicates the expected signs of the included j variables in a given X matrix. j NUMCOVER is the number of employees covered by the contract. It serves as a proxy both for negotiation costs, in that a larger bargaining unit implies that a more complex contract must be negotiated, and for union bargaining power, in that more workers can impose heavier strike costs on firms. It cannot be signed in the DUR equation since negotiation costs and union bargaining power are hypothe- sized to have opposing effects on duration. It should have a positive impact on both DWAGE and COLA U , however, since negotiation costs do not affect either variable and since greater union bargaining power should imply that a given union is able to win a larger wage increase and able to secure better protection against inflation. STRKEDAY is the number of days on strike leading up to an agreement. This variable, like NUMCOVER, proxies both negotiation costs and union bargaining power. One can surmise from mean strike length given in Table 1 that most contracts are negotiated without ever incurring a strike. To the extent strikes do occur, however, it is assumed that longer strikes are associated with higher negotiation costs and that longer strikes are inversely related to union bargaining power. 14 It is expected then that contract duration and strike length will be positively related since a long strike implies both high cost of negotiation and low union bargaining power. It is also expected that strike length will be inversely related to DWAGE and COLA U since a longer strike implies less union bargaining power. MULTIEMP is a dummy variable for whether or not the contract covers multiple employers. This variable should be directly related to negotiation costs, since negotiating a contract to cover multiple employers entails more complex negotiations, and should be inversely related to union bargaining power, since organization of employers implies greater firm bargaining power, other things being equal. It is hypothesized that the variable has a positive impact on contract duration and a negative impact on the likelihood that a cost of living clause is incorporated in the contract. REGDUR and INDDUR are, respectively, the average contract duration in the Ž . relevant region Northeast, North Central, South, or West and in the relevant, Ž . broadly defined industry manufacturing, non-manufacturing, or public sector in 14 A firm is likely to settle a contract quickly if the union has strong bargaining power and the firm will be able to withstand a long strike if the union has limited bargaining leverage. the quarter in which the contract is signed. These variables are included to control for the possibility that firm-union bargaining pairs emulate other bargaining pairs in their region or in their industry, thus both variables are expected to be positively related to contract duration. 15 REOPENER is a dummy variable for whether or not the contract contains a reopener clause. Contract reopeners act as another means by which bargaining pairs deal with uncertainty. That is, if unexpected inflation occurs over the life of the contract, then the contract can be reopened to adjust the wage appropriately. Thus it is expected this variable will be negatively related to the rate of wage change and that the probability that the contract will contain a cost of living adjustment clause will be lower since the reopener serves much the same purpose as the COLA clause. LVEXPINF is the expected rate of inflation from the Livingston index of inflation expectations for the period in which the contract is signed. Because workers care about real compensation, this variable should be positively related to the annual rate of wage change negotiated in the contract. It should, moreover, be positively related to the likelihood that the contract contains a COLA clause since expected inflation and unexpected inflation are likely to be positively correlated. UDIFFLAG is included as a proxy for excess demand conditions. It is the state unemployment rate minus the state natural rate of unemployment in the year before the contract is signed. 16 The larger is this variable the weaker is the economy in the state in which the agreement is signed; therefore, it is expected that DWAGE will be inversely related to this variable and also that it will be less likely that the contract will contain a COLA clause. Ž PDOT and PDOTLAG are the annualized quarterly inflation rates based on the . GNP deflator in the quarter in which the contract was signed and in the immediately preceding quarter. These variables reflect current and past inflation but also may serve as proxies for expected future inflation; therefore, both variables enter the DWAGE and COLA U equations with positive signs. AFLCIO is a dummy variable for whether or not the union is affiliated with the AFL-CIO. The maintained hypothesis is that unions affiliated with the AFL-CIO have greater bargaining power. Thus one would expect that affiliated unions will have a greater likelihood of securing a cost of living clause in a contract than will non-affiliated unions. 15 An anonymous referee points out, however, such positive association could also result if REGDUR and INDDUR proxy for unmeasured variables in the region or industry that all bargaining pairs, including the bargaining pair of interest, are responding to. 16 The state’s natural rate of unemployment was obtained by regressing the state unemployment rate against the national rate of unemployment and against a cubic function of time. The national natural rate of unemployment was then plugged into the equation along with the appropriate time value in order to generate an estimate. Table 1 Means and standard deviations Number of observationss1876. Variable Description Expected signs Mean U Žstandard DUR DWAGE COLA . deviation Endogenous Õariables a Ž . DUR Contract length in months = q q 29.55 9.40 a Ž . DWAGE Annual percent change in wage q = q 3.65 2.81 rate specified by contract a Ž . COLA s1 if contract contains escalator q y = 0.171 0.377 clause, s 0 otherwise Uncertainty Õariables b,d Ž . INFUNCRT Nominal uncertainty measure y q q 2.688 0.104 b,d Ž . URUNCERT Aggregate real uncertainty measure q y = 9.232 0.906 c,d Ž . RLURSDLG Real uncertainty measure for local q q = 0.755 6.846 labor market b,d Ž . RELUNCRT Relative price uncertainty measure y = y 9.904 0.219 Additional exogenous Õariables a NUMCOVER Number of workers covered ? q q 4482.99 Ž . by contract 16408.61 a Ž . STRKEDAY Number of days on strike prior to q y y 2.57 19.08 signing of contract a Ž . MULTIEMP Dummy variable indicating whether or q = y 0.077 0.267 not contract covers multiple employers d Ž . REGDUR Average contract duration in q = = 29.79 2.856 bargaining pair’s census region d Ž . INDDUR Average contract duration in q = = 29.62 3.353 bargaining pair’s broadly defined industry a Ž . REOPENER Dummy variable indicating whether or = y y 0.102 0.302 not contract contains a reopener clause a Ž . FRSTCONT Dummy variable indicating whether or = = y 0.213 0.410 not contract is first contract signed by bargaining pair a,e Ž . AFLCIO Dummy variable indicating whether or = = q 0.74 0.439 not union is affiliated with AFL-CIO b Ž . LVEXPINF Expected rate of inflation for period in = q q 4.692 1.045 which the contract was signed c,d Ž . UDIFFLAG State unemployment rate minus = y y 0.237 1.081 state natural rate of unemployment b Ž . PDOT Annualized inflation rate for quarter in = q q 3.695 1.924 which contract is signed b Ž . PDOTLAG Annualized inflation rate for quarter = q q 3.671 1.604 prior to signing of contract Ž . NONDRMFG Dummy variable for non-durable = ? ? 0.125 0.331 manufacturing Ž . MINING Dummy variable for mining = ? ? 0.002 0.046 Ž . CONSTRUC Dummy variable for construction = ? ? 0.041 0.198 Ž . Table 1 continued Variable Description Expected signs Mean U Žstandard DUR DWAGE COLA . deviation Additional exogenous Õariables Ž . TPU Dummy variable for transportation = ? ? 0.146 0.353 and public utilities Ž . WRT Dummy variable for wholesale and = ? ? 0.027 0.163 retail trade Ž . FIRE Dummy variable for finance, insurance, = ? ? 0.0064 0.080 and real estate Ž . SERVICES Dummy variable for services = ? ? 0.283 0.451 Ž . PUBADMIN Dummy variable for public = ? ? 0.223 0.416 administration Ž . NRTHEAST Dummy variable for northeast region = ? ? 0.235 0.424 Ž . MIDWEST Dummy variable for midwest region = ? ? 0.237 0.425 Ž . SOUTH Dummy variable for south region = ? ? 0.183 0.387 Ž . WEST Dummy variable for west region = ? ? 0.216 0.412 a Current wage developments. b CITIBASE database. c Statistical Abstract of the United States, various issues. d Tabulation by author. e Directory of National Unions and Employee Associations. Dummy variables for one-digit industries and for the major census regions are also included to serve as additional control variables in the auxiliary DWAGE and COLA U equations. The base industry is durable manufacturing and the base region Ž is the national level i.e., most contracts cover workers in a given region, but about . 13 of contracts cover workers at the national level . 5.3. Empirical results Ž . Ž . Table 2 presents the regression results for Eqs. 1 – 3 . Both results from Heckman’s consistent method of obtaining parameter estimates for a simultaneous equation, generalized probit model and Amemiya’s more efficient, generalized least squares method are presented and will be discussed. Before moving to a discussion of the estimation results for specific equations, it is interesting to compare coefficient values and t-statistics across the two techniques. Generally speaking, differences between coefficient values for a given independent variable in a specific equation are small when compared by technique. So, for example, the coefficient on wage change in the duration equation is y0.454 using the Heckman estimator and is y0.446 using the Amemiya estimator. T-statistics also exhibit little variation by technique. Casual examination of Table 2, moreover, reveals no particular pattern in absolute size of the t-values when compared by technique. In other words, the t-statistics decrease slightly in absolute value in some cases when the Amemiya technique is used, but increase slightly in the case of other variables. Table 2 Ž . Regression results t-statistics are in parentheses U Ž . Ž . Ž . Variables 1 DUR 2 DWAGE 3 COLA Heckman Amemiya Heckman Amemiya Heckman Amemiya Endogenous DURATION – – y0.018 y0.021 0.059 0.055 Ž . Ž . Ž . Ž . y0.39 y0.47 2.95 2.82 DWAGE y0.454 y0.446 – – y0.414 y0.431 Ž . Ž . Ž . Ž . y2.31 y2.26 y1.28 y1.33 COLA 0.399 0.411 0.678 0.702 – – Ž . Ž . Ž . Ž . 1.19 1.22 0.92 0.95 Exogenous CONSTANT 34.245 34.272 y5.214 y5.136 y13.848 y14.179 Ž . Ž . Ž . Ž . Ž . Ž . 2.32 2.32 y1.92 y1.89 y1.80 y1.85 NUM-COVER 0.0164 0.0162 y0.00436 y0.00472 0.0108 0.011 Ž . Ž . Ž . Ž . Ž . Ž . Ž . in thousands 1.34 1.33 y0.50 y0.54 2.13 2.17 STRKEDAY 0.019 0.019 y0.007 y0.007 y0.004 y0.004 Ž . Ž . Ž . Ž . Ž . Ž . 1.92 1.92 y2.07 y2.06 y1.31 y1.32 MULTIEMP 0.021 0.031 – – 0.007 0.020 Ž . Ž . Ž . Ž . 0.03 0.04 0.04 0.09 REGDUR 0.923 0.923 – – – – Ž . Ž . 12.30 12.29 INDDUR 0.683 0.683 – – – – Ž . Ž . 8.12 8.11 INFUNCRT y5.002 y5.018 3.987 4.033 0.643 0.669 Ž . Ž . Ž . Ž . Ž . Ž . y2.03 y2.04 2.11 2.13 0.79 0.82 RLURSDLG y0.015 y0.015 0.019 0.019 – – Ž . Ž . Ž . Ž . y0.52 y0.53 1.66 1.66 URUNCERT 0.544 0.548 y0.531 y0.539 – – Ž . Ž . Ž . Ž . 2.23 2.24 y1.86 y1.89 RELUNCRT y4.234 y4.234 – – 1.004 1.045 Ž . Ž . Ž . Ž . y3.93 y3.93 1.84 1.92 REOPENER – – y1.213 y1.184 y1.359 y1.351 Ž . Ž . Ž . Ž . y2.10 y2.05 y2.46 y2.45 FRSTCONT – – – – 0.001 0.017 Ž . Ž . 0.01 0.10 AFLCIO – – – – 0.088 0.094 Ž . Ž . 0.50 0.54 LVEXPINF – – 0.354 0.355 0.172 0.186 Ž . Ž . Ž . Ž . 2.02 2.03 0.77 0.83 UDIFFLAG – – y0.107 y0.108 0.063 0.064 Ž . Ž . Ž . Ž . y1.09 y1.10 1.11 1.13 PDOT – – y0.038 y0.040 0.026 0.026 Ž . Ž . Ž . Ž . y0.37 y0.40 0.60 0.58 PDOTLAG – – y0.088 y0.092 0.069 0.064 Ž . Ž . Ž . Ž . y0.81 y0.84 1.41 1.32 NRTHEAST – – 2.031 2.046 0.090 0.130 Ž . Ž . Ž . Ž . 3.83 3.86 0.16 0.22 Ž . Table 2 continued U Ž . Ž . Ž . Variables 1 DUR 2 DWAGE 3 COLA Heckman Amemiya Heckman Amemiya Heckman Amemiya Exogenous MIDWEST – – 1.460 1.468 0.206 0.225 Ž . Ž . Ž . Ž . 4.17 4.19 0.50 0.55 SOUTH – – 1.514 1.517 0.257 0.267 Ž . Ž . Ž . Ž . 4.28 4.29 0.58 0.61 WEST – – 1.219 1.225 0.279 0.287 Ž . Ž . Ž . Ž . 3.92 3.94 0.73 0.75 MINING – – 0.095 0.096 y0.444 y0.490 Ž . Ž . Ž . Ž . 0.07 0.07 y0.52 y0.57 CONSTRUC – – y1.772 y1.772 y1.907 y1.990 Ž . Ž . Ž . Ž . y2.40 y2.40 y2.12 y2.22 NONDRMFG – – 1.559 1.584 y0.912 y0.913 Ž . Ž . Ž . Ž . 1.73 1.76 y3.59 y3.59 TPU – – 1.758 1.766 y0.179 y0.182 Ž . Ž . Ž . Ž . 3.00 3.02 y0.45 y0.45 WRT – – 0.766 0.807 y1.695 y1.695 Ž . Ž . Ž . Ž . 0.63 0.67 y5.52 y5.52 FIRE – – 1.426 1.435 y0.233 y0.245 Ž . Ž . Ž . Ž . 1.48 1.49 y0.40 y0.42 SERVICES – – 3.651 3.677 y0.752 y0.760 Ž . Ž . Ž . Ž . 2.67 2.69 y0.95 y0.96 PUBADMIN – – 2.880 2.912 y1.020 y1.033 Ž . Ž . Ž . Ž . 2.15 2.18 y1.86 y1.88 2 R 0.205 0.205 0.198 0.198 – – Finally, the R 2 s in the equations for the continuous variables exhibit no apparent change whatsoever by technique. 17 Because the focus of this study is contract duration, I shall proceed by first Ž . discussing in detail the regression results for Eq. 1 and then conclude with a briefer discussion of the results for the wage change equation and the indexation Ž . equation. Of the two right-hand-side endogenous variables in Eq. 1 , only the rate of wage change has a significant impact on contract duration. Contracts specifying Ž higher rates of annual wage change tend to be somewhat shorter in length the . implied elasticity is small, however, at y0.055 . The indexation variable has the expected sign but is not statistically significant. Of the exogenous variables not related to economic uncertainty, the average Ž . Ž . contract duration found in the region REGDUR and in the industry INDDUR exert the strongest influence on the length of contract signed by a bargaining pair. 17 Though one does find differences if the calculation is carried to higher decimal places than reported in the table. A one month increase in average duration in the region is associated with nearly a one month increase in bargaining pair specific contract length, while at the industry level an extra month is associated with more than an additional half of a month of duration. These results suggest that bargaining pairs tend to emulate other bargaining pairs in the relevant region and industry. Table 2 also reveals that Ž . strike length STRKEDAY has a marginally significant impact on contract duration. Thus, if a bargaining pair has endured a strike, the parties to the agreement sign a contract of longer duration in order to amortize the cost imposed by the negotiation process over a longer period. Turning now to the economic uncertainty variables, Table 2 indicates that three of the four uncertainty variables are statistically significant. Only the measure of Ž . sectoral real uncertainty RLURSDLG is not significant. Consistent with the theoretical prediction of Gray and of Danziger and consistent with most of the Ž empirical work on the subject with the exception of the Wallace and Blanco . Ž . study , the variable measuring nominal uncertainty INFUNCRT is negative and highly significant. The implied elasticity is y0.46. The main contributions that Danziger’s work makes to the contract duration literature are the predictions that uncertainty concerning aggregate real shocks lengthens labor contracts by increasing workers’ desire to insure themselves against such shocks and that relative shocks should shorten labor contracts. The results presented in Table 2 support both of these hypotheses. Specifically, the coefficient on the measure of real uncertainty, URUNCERT, is positive and highly significant. The implied elasticity for this variable is 0.17. Though the magnitude of response of contract duration appears to be stronger toward nominal shocks, real shocks nevertheless do lengthen contracts as the theory suggests. In addition, the coefficient on the relative uncertainty variable, RELUNCERT, is negative and highly significant. Its elasticity is y1.42. Thus contract lengths appear to be most responsive to relative price uncertainty across sectors. This may be because relative uncertainty between consumer and producer prices provides strong induce- ments for both union and firm to sign short contracts. Turning now to the results for the other two equations, Table 2 shows that neither the length of contract nor whether the contract is indexed to the cost of living have a statistically significant impact on the annual rate of wage change Ž . negotiated in the contract. Results for the exogenous variables in Eq. 2 are interesting. For example, contracts preceded by strikes tend to have lower rates of wage change. This is consistent with the notion that firms take strikes in order to Ž Ž .. diminish union wage demands Ashenfelter and Johnson 1969 . Table 2 also Ž . reveals, not surprisingly, that expected inflation LVEXPINF and the rate of wage change are positively related, with a 1 increase in expected inflation associated with more than a three-tenths percentage point increase in wage change. In Ž . addition, uncertainty regarding inflation INFUNCRT is directly related to the rate of wage change. This variable exerts a particularly strong influence on the rate of wage change in that its implied elasticity is 2.97. As noted above, one of the factors determining the degree of wage change negotiated in a contract is unexpected inflation. Accordingly, INFUNCRT may proxy as a signal of future unexpected inflation and also may serve to measure desire on the part of the union to catch up for past bouts of unexpected inflation. Uncertainty regarding real Ž . shocks URUNCERT is inversely related to the rate of wage change. The implied elasticity for this variable is y1.36; therefore, as the efficient risk sharing hypothesis suggests, real uncertainty moderates either worker wage demands or firms willingness to meet worker wage demands. Finally, the coefficients on the Ž . regional dummies in Eq. 2 are interesting in that they are positive and signifi- cant. The implication of this result is that workers signing contracts at a local or regional level are paid a premium vis-a-vis workers signing contracts at a national level. The difference can be as small as 1.2 percentage points in the West and as large as 2 percentage points in the Northeast. Since bargaining unit size is held constant in the regression, this result may simply imply that unions negotiating contracts on behalf of a bargaining unit of given size at the national level have less bargaining power vis-a-vis unions negotiating on behalf of same sized bargaining units at a more region specific level. Ž . Eq. 3 , the indexation equation, indicates that contracts of longer duration are more likely to be indexed. The effect of one additional month of contract length on the probability that the contract is indexed is 0.0184. 18 This value translates to an elasticity of 3.19; therefore, as theory suggests, the likelihood of indexation is Ž . strongly related to the length of the contract. Estimation of Eq. 3 also reveals that Ž . if the contract contains a reopener clause REOPENER , then it is less likely that the contract will be indexed. This result holds because a reopener clause is an alternative means by which a firm and union can allow for the possibility of unanticipated inflation during the life of the contract. The table shows, in addition, Ž . that the larger the number of workers covered by a contract NUMCOVER , the higher the probability of indexation. The regression results also indicate that relative uncertainty between consumer prices and producer prices raises the probability of indexation. The lack of significance of the regional dummies suggests little systematic difference across the country in tendency to index. Finally, all of the industry coefficients are negative, four significantly so, which implies that firm-union pairs in durable goods manufacturing are more inclined to sign agreements containing COLA clauses. This result may owe to a pattern- bargaining phenomenon among such firms or it may be because such firms are in industries that tend to be more cyclically sensitive. 18 w x Ž X . Ž . Calculated as EE COLA rEx s f b x b, where f . is the standard normal density function. Setting continuous variables to mean values and assuming that the contract is not a first contract, does not contain a reopener, the union belongs to the AFL-CIO, the firm is a durable goods manufacturer, X Ž X . and the contract covers workers nationally yields b x sy0.588. Therefore, f b x b s 0.3352= 0.055s 0.0184.

6. Conclusion