Real Wage Chronologies

We process information in a large number of wage contracts, signed over a period of several decades, to generate the long-run history of the real wage for each bargaining pair. We term these hitherto unexamined histories 'chronologies'. We are able to generate 1574 continuous real wage chronologies and we examine the evolution of the real wage in each case. We explore the influence of productivity growth, the industrial relations record of the pair, the influence of industry and region as well as the initial wage on the growth of the real wage rate over the decades in the sample. We conclude that these economically important forces can be statistically discerned in the wage chronologies.


Introduction
For well over three decades now, economists have explored the unique and detailed information contained in wage contracts in order to take into account important institutional features of labour markets and in order to better understand how these important markets behave. The studies of Hamermesh (1970) and Sparks and Wilton (1971) pioneered the econometric exploration of US and Canadian collective bargaining agreements (respectively). Riddell (1979) is also in this tradition. With time, these explorations became broader and began to cover other provisions of wage contracts such as (i) the incidence and intensity of wage indexation issues, in inter alia Ehrenberg, San (1983, 1984), Card (1983Card ( , 1986, and Hendricks and Kahn (1983) and (ii) the duration of wage contracts, in inter alia Christofides and Wilton (1983), Vroman (1989), Murphy (1992Murphy ( , 2000, and Rich and Tracy (2004).
These are but a few examples of papers that deal with the major provisions of contracts, some addressing several features at the same time and, more recent ones, venturing into hitherto underappreciated aspects of collective bargaining -e.g. Hendricks and Kahn (1986), Cramton and Tracy (1992), Fortin (1996), Gu and Kuhn (1998), and Danziger and Neuman (2005).
Because the focus in these papers has been the information in collective bargaining agreements available in unbalanced panels over relatively short periods of time, these studies have overlooked a potentially informative aspect of the data which derives from the fact that the entire history of the collective bargaining agreements reached by a pair (a firm and a particular union) may be available over a very long period of time. It is, therefore, possible to see how important contract provisions for a given pair evolve over a matter of 1 decades.
To be sure, the concepts of unexpected and uncompensated inflation, in the sub-literature synthesized in Christofides (1987), for example, require that contracts be connected so that information from the previous contract can be allowed to influence the terms of the current agreement. However, this connection is between consecutive contracts only. Also, the examination in Christofides and Wilton (1985) of a possible wage 'explosion' in the aftermath of wage controls relied on linking contracts under controls with those signed by the same pair in the aftermath of controls. Finally, the papers on holdout pay particular attention to issues of timing between contracts. However, the entire contractual history for each pair can be linked together, revealing how important contract provisions change through time. The length of this history is limited only by the available sample length and by possible breaks in the relationship between pairs. It is therefore possible to speak of the 'chronologies' of contract provisions. Important provisions in contracts such as the real wage, contract duration and the elasticity of indexation can be traced out at the pair level through these chronologies. A number of questions that do not emerge naturally when the focus is individual contracts can be posed and answered. For instance, a real wage chronology would show how the real wage agreed to by a pair has evolved through long periods of time, whether it has grown secularly to reflect productivity growth, whether it depends on the industrial relations history of the pair, whether it differs from those agreed to by 'comparable' pairs and, if so, whether it ultimately converges to them. Chronologies could examine at the pair level whether secular increases in contract duration, which might render the macroeconomy less flexible, are pervasive - Christofides and Peng (2006) show that the average duration of contracts that became effective in each year has doubled between 1980 and 2000. A similar approach can deal with wage indexation issues and the apparent decline of indexation through time also noted in the above reference, a tendency that would work towards increasing real wage flexibility.
In this paper, we explore a particular long run feature of wage contracts, focussing on real wage chronologies. In section 2, the data used and the concept of a real wage chronology, as it derives from the contract data, are discussed; features of the derived chronologies are also examined. In section 3, the method used to examine these chronologies econometrically is presented and the results obtained are discussed in section 4. Conclusions appear in section 5.

Contract Data and the Wage Chronologies
The contract data used for this study is constructed from electronic records provided by Human Resources Development Canada (HRDC), as it was known when the data were released to us. This is the agency in charge of industrial relations in Canada. The data base contains information on 11885 contracts signed between 1976 and 2000 by firms which employ 500 or more employees. Each contract contains a unique identifier which allows us to string together all agreements signed by the same pair. In order to ensure the continuity needed in the chronologies, only contracts with an uninterrupted history are included in the analysis, leaving 8928 contracts available for analysis -construction contracts are also excluded because they were not part of the data until 1984. The HRDC data contain information on a number of variables, including the settlement, effective and expiry dates of the contract, the number of employees that it covers, the industry and region that it is located in, and the nominal base wage (including 'fold-ins' generated by the cost of living allowance clause (COLA) if any) at the end of the previous contract pexpwage. Information in the current contract makes it possible to generate the annual nominal wage percentage change (including COLA generated increases) · w and the duration of the contract measured as the difference between the expiry date and the effective date of the current contract, Duration, in months. The nominal wage level at the expiry date of the current contract may then be calculated as The nominal wage rates pexpwage and expwage are then converted into real terms using the values of the consumer price index at the expiry date of the previous contract (in most cases this is equal to the effective date of the current contract) and the expiry date of the current contract. Thus, the real wage level at the beginning and at the end of each contract are calculated in this way. Descriptive statistics on the variables used, by contract, are presented in Table 1 Figure 1 shows the real hourly contract wage calculated over all contracts whose effective date falls in a particular year. For comparison purposes, Figure 1 also shows real hourly earnings 1 from 1983 to 2000 -the period over which the latter series is available. The contract real wage series is higher and more volatile, especially during the 1990s. The relative position of the two series is not surprising given that contract wages come from large firms in the unionized sector. The greater volatility of the contract series reflects the turbulent period of industrial relations in the public (provincial and federal) sector during the period 1991 -1996, a period during which active wage control policies were pursued. In addition, the contract series is more likely to reflect idiosyncratic forces which average out in the aggregate.
Both series in Figure 1 show the remarkable stability in the unconditional real wage through time. Apparently, there has been no perceptible real wage growth over this period and, indeed, both series are below their starting values by the end of the period. One issue that is explored below is whether productivity gains have influenced wage growth during this period.
The HRDC data base includes a regional identification code and 3-digit SIC code which allow us to create seven regional dummy variables (Atlantic, Quebec, Ontario, Prairie, British Columbia, Territories and Multiprovince 2 ) and ten industrial dummy variables (Natural Resources, Manufacturing, Transportation, Communication, Utilities, Trade, Education, Health, 1 Hourly earnings are the CANSIM montly series V255025. They have been converted into real terms using the CPI index (P100000) and have been averaged by year. 2 Certain contracts cover more than one province and are thus multi-regional. Services and Others) that categorize each contract. Table 1 shows that most contracts are in Education (27%), followed by Manufacturing (20%), and in Ontario (35%). Figures 2 and 3 show the hourly real contract wage calculated over all contracts, whose effective date falls in a particular year, by SIC ( shows similar information to that in Figure 2 but on a regional basis. Contracts in the Atlantic provinces have the lowest real wages during most of 3 There is a widespread view that industry effects, which are significant in individual wage functions, cannot be easily explained by classical competitive theories of wage determination (see Slichter (1950), Thurow (1976), Wachtel and Betsey (1972) and Cain (1976)). Studies of wage determination based on human capital and mobility frictions typically leave substantial unexplained inter-industry or inter-firm wage differentials -see Dickens and Katz (1987) and Krueger and Summers (1988). Helwege (1992) shows that those differentials are not highly positively correlated with subsequent employment growth, as one could expect if they resulted from mobility frictions. Gibbons and Katz (1992) investigate the possibility that differentials are explained by unmeasured ability differences but do not have encouraging results. The more recent study by Walsh (1999) shows that the efficiency wage model can only explain a small fraction of the wage differentials that prevail accross industries. real wages -note that a common price index has been used to deflate across regions. Again, this ranking is consistent with stylized facts about regional disparities in Canada over the period studied. In the empirical work below we take into account possible industry and region effects. There is slight visual evidence of some convergence in the series of Figure 3, a general issue to which we return below.

Figure 2 Annual Average Hourly Real Wage by Industry From Contracts
The key innovation in this paper is arranging the contract data into pairbased chronologies. This is achieved by sorting the contracts using the unique  The third contract in the sequence begun in 1983; it was a two-year contract, and did entail real wage growth. The particular chronology discussed shows the changing pattern of contract duration for the pair involved and follows a slight upward trajectory. This is generally true of the other chronologies shown in Figure 4. There is considerable difference in the real wages paid by the top and bottom chronologies; in the case of Figure 4, this difference is more than ten real dollars per hour. This is noteworthy given that, in both cases, the real wage shown is the base wage for firms in manufacturing, albeit not necessarily firms of the same size and not necessarily paid to workers with similar skills who are represented by the same unions. It should be noted that this difference remains even if we confine Figure 4 to Ontario, thereby reducing (but not necessarily eliminating) an important part of regional disparities. A final feature of Figure 4 is that not all chronologies begin or end at the same time. We return to this issue in the empirical section below. Table 2 Table 1, as the average real wage at the expiry of the previous contract because it is calculated at an earlier point in time. 6 The fact that the 1980 average real wage of the completed chronologies exceeds the average real wage at the start of chronologies (row, 3 versus row 2 in Table 2) suggests that the real wage chronologies that have had to be projected back to 1980 entailed higher than average real wages. A variable that has an important long-run role in the wage determination process is productivity growth. The variable 'Prod' is is defined as the annual growth rate of an index of labour productivity over the length of each historical chronology. It was generated from Statistics Canada Table 383-0005 and was attached to the HRDC database using the three-digit SIC code and the effective date of the contract. Prod has a mean of 0.0171 and a standard deviation of 0.0183 over the chronologies in the sample - Table 2. While this average annual growth rate is modest, it would, over the two decades studied, justify a noticeable increase in the real wage rate. We examine whether what is apparently not evident in the averages plotted in Figures 2 and 3 can be a significant statistical force at the individual chronology level.
Another variable that may condition real wage outcomes in the long run is the professionalism and effectiveness of the industrial relations practices followed by the bargaining pair. These practices are not exercised in a vacuum but, rather, reflect the economic environment that the pair operates within.
A variable that may capture both aspects is the duration of negotiations between the pair Durneg leading up to the agreed upon contracts that make up the chronologies. In the HRDC data, this variable is measured as the length of time between the official notice to bargain and the settlement date for the contract. It has a mean of 8.18 months and a standard deviation of 4.37 months - Table 2. Tracy (1992, 1994) suggest that holdout, which is intimately related to Durneg, entails loss of productive efficiency which may then be reflected in wage growth. In a number of games, the pie gets smaller with delays in reaching agreement. We, therefore, take account of this variable in the empirical work below.
We also report, in rows 2 and 4 of Table 3, an alternative initial real wage and the average value of the duration of negotiations in the previous contract P durneg. These variables are used to deal with possible endogeneities in the regression analysis that follows -see the next section. For the moment, we note that, though they are independent of current-contract notions, they are close (in terms of descriptive statistics) to the variables that they will instrument.

Methodology
Having The forces of wage arbitrage and convergence would imply a negative relation between Grate and the initial real wage lnW 0 . However, measurement of this process could be complicated by unobservables. If, for example, the forces of managerial dynamism that make for sustained growth over time (such that Grate defined over the entire chronology is high) also imply conservative wage setting preferences on the part of the firm, the initial wage might also be unusually low. Thus, the initial wage when it is included as a regressor may be negatively correlated with the equation error term; if so, the estimator of the coefficient on lnW 0 will be biased. In order to avoid this possibility, we instrument (using Two Stage Least Squares) the initial 1980 wage for each chronology using a relevant average of starting wages which excludes the own wage for each particular chronology. This average is calculated at the detailed three-digit industry level (rather than the more aggregate level used in the regressions) and for the province (rather than the more aggregate region used in the regressions) within which each particular chronology is located -see row 4, Table 2. Its natural logarithm is used to instrument the natural logarithm of the initial real wage lnW 0 .
A similar complication may arise with respect to Durneg. If, for instance, large settlements that are due to unobservables take longer to negotiate, then the error term may be positively related to Durneg, leading to bias in the estimation of its coefficient. The potential problem here may not be severe: An unobservable that makes for a high wage settlement may not always involve long negotiations if it is acknowledged by both sides of the bargain. In addition, in the regressions that follow, Durneg is defined as an average over all the contracts signed by the pair in each chronology, thereby weakening the endogeneity mechanism. Nevertheless, we explore two robustness procedures: First, we proxy the industrial relations context within which the bargaining pair works with the previous-contract duration of negotiations (P durneg), see row 8, Table 2 for descriptive statistics. In an alternative approach, we treat P durneg as an instrument, in which case the predicted values for Durneg and lnW 0 in Two-Stage-Least Squares are constructed from all exogenous variables as well as the two instruments.
These specifications are explored in the appendix Table A1. All estimation is carried out with SAS.
In all cases, the average number of employees in each chronology is used to weight the data for each chronology. Table 3 contains the estimates obtained. Results I-III refer to weighted OLS regressions where the possible endogeneity of lnW 0 is not taken into account.

Empirical Results
Result I reports the regression of Grate on an intercept, P rod and Durneg only. P rod has the expected positive coefficient and it is significantly different from zero at the 1% level. Durneg has a negative coefficient which is significantly different from zero at the 1% level. When the logarithm of the initial wage is added, in Result II, the estimates on the coefficients of P rod and Durneg are not substantially altered and the initial wage has a negative coefficient which is significantly different from zero at the 1% level. The Using the estimates in Result V, it is worth considering the quantitative importance of the estimates for the explanatory variables P rod, Durneg and lnW 0 . An increase in P rod by one standard deviation (0.0183 in Table   2) would have the effect of increasing Grate by 0.000926 (0.0506×0.0183).
This is approximately 29% of the mean value of Grate (0.0032) in Table 2.
While this is not an enormous effect, it is not negligible either. Thus, the average annual productivity growth experienced over a chronology does have a measurable effect on the average annual growth rate of real wages over a chronology. An increase in Durneg by one standard deviation (4.37 in Table   2) would decrease Grate by 0.000874 (-0.0002×4.37), an effect comparable to that of an increase in P rod by one standard deviation. Thus, the ability of the pair to work effectively at the bargaining table does appear to have an impact on the real wage fortunes of the pair. Finally, an increase in lnW 0 by one standard deviation (0.25 in Table 2) would decrease Grate by 0.00455 (-0.0182×0.25). This suggests, relative to the productivity effects, substantial effects through the convergence processes. The effects of the convergence calculations are about five times as large as those for productivity.
While the economic case for the endogeneity of Durneg is not overwhelming, it is important to examine whether the conclusions reached above are robust to the procedures outlined in the previous section. In general, these robustness checks are favourable and we, therefore, confine their detailed presentation to an appendix. Note that a Hausman (1978) specification test accepts the equality of the OLS and IV estimates. Table A1 reports details of these checks. In the first regression, the variable Durneg is replaced by P durneg. The estimated coefficient (-0.0004) is equal to that reported as Result I in Table 3. When the instrumented version of lnW 0 is added to the P rod and P durneg, the estimated coefficient (t value) is, at -0.0157 (-10.21) very similar to Result IV in Table 3. This is also true when industry and region effects are included (columns 5 and 6, Table A1). In the alternative robustness check, P durneg is used as an instrument for Durneg (columns 7 to 12, Table A1), while lnW 0 continues to be instrumented as described above. In column 7, Table A1, the estimate for the coefficient on Durneg is higher and that for P rod lower than in column 1, Table A1. However, this difference disappears in the more complete specifications: In the most complete specification (columns 11 and 12, Table A1) Durneg entails a coefficient (-0.0002) which is identical to that in column 9, Table 3, albeit with a t value which, at -1.97, indicates significance at the 5% but not the 1% level.
The coefficients on Prod and lnW 0 continue to have the expected signs and be significant at the 5% level but they are somewhat lower in absolute values relative to those in column 9, Table 3. Thus, the calculations for their quantitative significance discussed above may present maximal impacts. Industry effects in these regressions are not much affected, though the regional effects display two noteworthy changes, namely the now (relative to Result V, in Table 3) significantly lower growth in real wages in Quebec and British Columbia relative to multi-province chronologies.

Conclusion
In this paper, we take a fresh look at the information contained in the repeated wage agreements struck by bargaining pairs over more than two decades with the view to examining, not the collective bargaining outcomes at a point in time that have been studied so far, but the long run outcomes implied in these bargains. This focus on the outcomes of individual bargains complements studies at more aggregative levels. While a number of outcomes such as contract duration and indexation can in principle be considered, we focus on real wage chronologies that trace out the long run pattern of real wages for each pair in the sample. This is an approach that has not been followed so far and one that, hopefully, casts light on the long run behaviour of the all-important notion of the real wage.
We generate the average annual growth rate in the real wage for each chronology and study the influence of productivity growth, the speed with which the bargaining pair can reach agreements and the initial wage on this growth rate. We do so controlling for and estimating industry and region effects that are consistent with intensification of the stylized facts on interindustry and regional wage patterns. We find that productivity growth and the bargaining skills of the pair influence the long-run growth in the real wage. Convergence in real wages, controlling for the other variables mentioned above, appears to be at work and it appers to be quantitatively strong.
The results in this paper pertain to the unionised sector, of course. While long run analysis of this kind is only possible because of the nature of the information in this sample, the results obtained may illuminate behaviour in the broader economy. Christofides and Stengos (2003, footnote 8) report that the employees covered by this data represent 11% of the Canadian labour force. To the extent that similar results hold for contracts involving small numbers of employees (these are not represented in the data sources that we tap), our findings would be more broadly applicable. It is worth recalling that, in contrast to the US, union membership in Canada as a proportion of non-agricultural employment is relatively high (32% in 1999). As longer panels on individuals become available, it would be interesting to focus on the long run labour market experience of individuals, appropriately averaged over wide-enough groups to remove idiosyncratic effects. To our knowledge, these individual-based chronologies have not been studied and it is hoped that this paper may help stimulate interest in that direction.