NORC at the University of Chicago Union Wage Differentials in the Public and Private Sectors: A Simultaneous Equations Specification Author(s): Chris Robinson and Nigel Tomes Source: Journal of Labor Economics, Vol. 2, No. 1 (Jan., 1984), pp. 106-127 Published by: The University of Chicago Press on behalf of the Society of Labor Economists and the NORC at the University of Chicago Stable URL: http://www.jstor.org/stable/2535019 Accessed: 29-03-2018 09:06 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms NORC at the University of Chicago, Society of Labor Economists, The University of Chicago Press are collaborating with JSTOR to digitize, preserve and extend access to Journal of Labor Economics This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms Union Wage Differentials in the Public and Private Sectors: A Simultaneous Equations Specification Chris Robinson, University of Western Ontario Nigel Tomes, University of Western Ontario and Economics Research Center, NORC The paper attempts to integrate new approaches to estimating union wage effects with the analysis of public-private sector wage differentials. Estimates of the union differential in both public and private sectors, allowing for the endogeneity of union status, are presented. The hypothesis that the recently measured rents to public sector employment primarily reflect the recent increase in unionization in that sector is examined, and receives considerable empirical support. There was evidence of positive selection into the union sector, especially for private sector workers. Union status appears to be strongly influenced by the expected wage gain from joining the union sector. I. Introduction The estimation of wage differences associated with unionism has reemerged recently as a controversial topic. A general consensus, based implicitly or explicitly on some form of the monopoly theory of unionism, appeared to have been achieved in the 1960s. Gregg Lewis (1963) summarized and reanalyzed the large body of U.S. literature on the wage We have benefited from discussions with James Davies, James Heckman, and Glenn MacDonald. Helpful comments were provided on an earlier draft by members of the Labour Economics Workshop at the University of Western Ontario, the Quantitative Economics Workshop at Queen's University, and the 1983 Labour Economics Conference at McMaster University. [Journal of Labor Economics, 1984, vol. 2, no. 1] (? 1984 by The University of Chicago. All rights reserved. 0734-306X/84/0201-0005$01.50 106 This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms Union Wage Differentials 107 effects of unions. His finding of a wage difference on the order of 10%- 15% represented the consensus view of the effects of unions. Since that time, however, as a result of studies emphasizing the endogenous nature of union status the consensus has disappeared. These studies were recently reviewed by Parsley (1980) and by Freeman and Medoff (1982). The key studies in this area include those by Ashenfelter and Johnson (1972), Duncan and Stafford (1981), Schmidt (1978), and Lee (1978). Both Ashenfelter and Johnson (1972) and Schmidt (1978) demonstrate that the positive effect of unions on wage rates found in single-equation studies can be eliminated in a simultaneous equations framework. Lee (1978) postulated an explicit model of individual choices regarding union status and used this to "correct" for selectivity bias in separate union and nonunion wage equations. The correction reduced the estimated effect of unions, but only by a modest 2 percentage points. This paper seeks to integrate the new approach to unions with the analysis of public-private sector wage differentials. The literature on public sector wage effects is not as large as that on unions. However, because of the increasing size of the public sector, the importance of this topic is growing. Recent studies have been conducted by Ashenfelter and Ehrenberg (1975), Smith (1977), and Borjas (1980) for the United States and by Cousineau and Lacroix (1977), Gunderson (1979a, 1979b), and Auld et al. (1980) for Canada. One of the major findings is that the public sector appears to have a less elastic demand curve for labor. Gunderson (1979a, 1979b) reports that rents are being earned in the Canadian public sector, especially by women and less skilled workers. Similar premia associated with public sector employment are reported by Smith (1977) for the United States. A natural question that arises from consideration of these recent results is whether the public sector rents merely reflect the usual union wage effects. This is the first study that allows for the determination of union sector status in estimating both potential union-nonunion and publicprivate sector wage differentials. In addition, the hypothesis that the recently measured rents to public sector employment are simply due to greater unionization in that sector is examined. Finally, this is also the first study to provide selectively corrected estimates of union wage differentials for Canada based on individual data.1 The plan of the paper is as follows. In Section II the determinants of union status are considered and the union wage differential is estimated i As a by-product of their study of migration, Grant and Vanderkamp (1980) produce an estimate of the payoff to union membership using individual micro data. However, their definition of union status differs from the conventional one by including members of professional organizations. Starr (1973) analyzes wages by establishment in Ontario. The few remaining studies (Kumar 1972; Maki and Christensen 1979; MacDonald and Evans 1981) employ aggregate industry data. This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms 108 Robinson/Tomes on the assumption that public sector status is exogenous. Estimates of the union wage differential for Canada, which may be compared with recent work on individual data sets for the United States, are presented. These show large differentials, especially for male workers. Union differentials in the public sector are broadly similar to those in the private sector. Thus the hypothesis that union premia are larger in the public sector because of a less elastic demand curve receives little support. Section III examines the public-private sector differential. Controlling for union status there is little evidence of public sector rents. However, because of the high proportion of unionized workers in the public sector, a substantial positive premium is estimated when union status is not controlled for. This provides evidence for the hypothesis that recently estimated rents accruing to public sector workers are in fact union differentials. Finally, Section IV summarizes the conclusions of the analysis. II. Union-Nonunion Wage Differentials and the Probability of Union Status If unions are in a monopoly position they must limit entry, thus producing a queue. In order to observe an individual in a union two criteria must be satisfied. First, the individual must have chosen to enter the queue; second, the individual must have been picked out of the job queue by the unionized firm. Because of the lack of information on the relevant populations for the two selection stages (e. g., which workers offered themselves to the union sector but were not chosen, etc.), previous authors have collapsed the process into a single criterion for union status. In this paper we follow the same procedure. Following Lee (1978) we assume that worker i has a "reservation wage," pi, for joining the unionized sector. The worker joins the union if WUi- WNi > p,, (1) WN, where Wu, and WN, are the wage rates that worker i receives in the union and nonunion sectors, respectively. The reservation wage, Pi, combines both the monetary costs of unionization implicitly or explicitly borne by the worker and the value an individual attaches to being inside or outside a union because of differences other than the wage levels in the two sectors. The costs of unionization are assumed to be high for employees with high turnover rates. Thus Lewis (1959) argues that unionism is more likely to be successful for full-time male workers than for females or casual workers. To the extent that unions restrict entry by non-pricerationing other individual characteristics, determining the attractiveness This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms Union Wage Differentials 109 of the individual to the uni cost to the worker. These are assumed to include education, experience, and sex. Since different regulations governing union-management relations differ across provinces, geographical location may also be expected to influence the costs of unionization. If, as has been argued by Ashenfelter and Johnson (1972) and others, union services are normal goods, pi will be smaller the higher the level of the spouses' income. Finally, assuming economies of scale in organizing workers, the costs of unionization will be smaller for workers attached to industries with large plant sizes. The discussion of the previous paragraph may be summarized by the following criterion for union status: - -WN- (In Wu - In WN) > X43 + E. (2)WN l 1 where Xi is a vector of ch schooling, experience, language, sex, part-time worker, marital status, income of spouse, and average plant size of the industry in which the individual works.2 The disturbance E, represents unobservable characteristics of the individual that affect p,. These are assumed to follow a normal distribution with zero mean and variance Se. Given this assumption the choice between union and nonunion status may be put in a standard probit form. An individual will be a union member if I > 0 where Ii = (In Wu, - In WN ) - Xi4 - E i (3) Wage rates in the union and nonunion sectors, respectively, a to be given by the standard semilogarithmic forms In Wu, Xui'Yu + Eui (4) and In WN XN OOO'Oq r q YXNOo???~~~~000000U')00*>V) v ) or u q cN "D ,I c 00 00 00 , 71 "I C) N N N o) ,I o ON O N q on o3 U or o C) u e + 0 04 0 0 +.~ .: ',. .: .: .: . : .~ . ',. ',. . ...a :~~~~~~r I- C) ON g g = =N=9;=N' This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms Union Wage Differentials 121 estimate for the wage diff there is no strong evidence and private sectors. As expected, the pure "cost" variables, plant size and part-time status, have essentially identical effects in the structure as in the reduced form. In addition, the structural coefficients for marital status and spouse's income are the same as the reduced-form coefficients. Thus the evidence in favor of unions providing normal goods, at least in the private sector, is maintained. The major differences between the reduced-form and structural coefficients appear for variables that influence wage rates as well as (potentially) costs. Most notably the effect of being male, which is strongly significant in the reduced forms, is eliminated in the structure. This suggests that most of the higher probability of males belonging to unions is due to the larger expected wage gain as compared with females. Similarly, the regional differences apparent in the reduced forms are absent in the structure. Since union legislation is a provincial matter, union costs may potentially vary by province; however, comparison of the results in tables 6 and 7 suggests that any cost differences are dominated by differential Table 7 Public-Private Sector Wage Differentials for Selected Groups of Hourly Paid Workers Corrected Coefficients Uncorrected Coefficients -fg fpg (g pg Union sector: Males: Unskilled - 12.58 - 7.49 - 2.70 - 4.88 Semiskilled - 7.20 - 7.49 .30 - 4.88 Skilled - 9.06 - 7.49 - 2.68 - 4.88 Average - 9.34 - 7.49 -1.18 - 4.88 Females: Unskilled - 6.22 2.11 - .84 2.34 Semiskilled - .44 2.11 2.22 2.34 Skilled 2.44 2.11 - .82 2.34 Average - 2.24 2.11 .71 2.34 Male and female average - 6.72 - 3.94 - .48 - 2.21 Nonunion sector: Males: Unskilled 2.00 - 22.24 -11.61 - 4.34 Semiskilled 6.65 - 22.24 -1.25 - 4.34 Skilled 18.70 - 22.24 7.93 - 4.34 Average 8.83 - 22.24 -1.13 - 4.34 Females: Unskilled 14.63 - 2.22 10.06 21.88 Semiskilled 19.85 - 2.22 22.96 21.88 Skilled 33.39 - 2.22 34.39 21.88 Average 22.30 - 2.22 23.11 21.88 Male and female average 17.59 - 9.23 14.63 12.70 NOTE.-Average skill levels use the full sample weights. A level of 67.8% of organized workers is assumed for the private sector in computing fi. The pooled wage equations automatically hold the level of organization the same across public and private sectors. The differential is computed as dig-(In Wg - In Wp) - 1, where In Wg and In W are the natural logarithms of wage rates in the public and private sectors, respectively. Male and female averages weight the differential by the proportion of public sector males and females in each sector. This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms 122 Robinson/Tomes wage levels by province. However, public sector status has a positive effect on the probability of union status in both the reduced form and the structure. This suggests that the higher percentage of unionization in that sector is not due solely to larger potential wage gains, but also reflects differences in the costs of organization. The significant wage difference coefficients in table 6 for private sector workers are quite similar to those obtained by Lee (1978). Lee does not discuss the interpretation of this coefficient in terms of what model parameters it estimates. However, the conformity of the present results with those of Lee suggests that this issue should be pursued further. Substituting (4) and (5) into (3) indicates that the coefficient on the wage equation is the inverse of the standard deviation of a linear combination of the wage equation disturbances, Eu and EN, and E, the disturbance in the "costs" or reservation wage equation. Thus the coefficient on the wage difference depends on the variances and covariances of Eu, EN, and E. Since there is a large literature on estimates of variances of disturbances in individual logarithmic wage equations, it would be of interest to know whether the wage difference coefficients in table 6 were consistent with the stylized facts on these variances. Estimating the variances of Eu and EN is not possible directly because of the problem of censored samples. However, we can obtain predicted values of Eul, and EN, for all members in the sample (see Robinson and Tomes 1983, n. 15). Using these predicted values, the implied variances for Eu and EN are .02 and .06, respectively. The covariance is -.03. The estimated variances are underestimates since they use expected rather than actual values. Inspection of variance estimates in the literature suggests that these results are not inconsistent with that literature. For example, variances of individual components in wage equations are often estimated in the range .10-.15. (See MacDonald and Robinson 1982.) III. Public-Private Sector Wage Differences Recent estimates of wage differentials for public versus "comparable" private sector employees suggest positive premiums for public sector workers. Smith (1977) found substantial positive premiums for federal government workers in the United States in 1975. For males the differential was 13/%-15O%; for females the differential was 18%-20%. For state and local government employees, however, the differentials were only positive for females. Gunderson (1979a, 1979b) computed wage differences between public and private sector workers in Canada using a methodology similar to that of Smith's U.S. study. Gunderson did not distinguish between different levels of government. He found results similar to those of Smith. The public sector differential was typically positive but larger for females (8.6%) than for males (6.2%). Because of data limitations, Gunderson was unable to take into account the effects This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms Union Wage Differentials 123 of unionization. This is a potentially serious drawback because union coverage is considerably higher in the public than in the private sector. Thus public sector differentials may be confused with union differentials. Estimates of public sector differentials, controlling for union status, may be obtained from the wage coefficients presented in tables 2 and 3. However, these estimates, like previous studies, assume public sector status is exogenous. If, in fact, the choice of sectors is endogenous these estimates will be subject to bias. In order to avoid this two strategies were pursued. First, a model of public sector choice was specified and estimated to correct the estimates. Second, the instrumental variables approach was pursued by using the linear probability model to obtain an instrument for public sector status in equation (6). There were several problems encountered in undertaking these procedures due to the poor performance of the probit equation for determining public sector choice, or more generally of poor instruments for public sector status. Adopting a compromise solution to these problems yielded wage equations in general very similar to those obtained correcting only for union status (see Robinson and Tomes [1983] for further details). Some confidence may be placed in the equation determining union status, because of its similarity with those obtained by other investigators. Since a satisfactory equation determining public sector status could not be obtained, the analysis of public sector differentials in this section is based on the wage equations of Section II. The estimated wage equations from the pooled private and public sector sample provide a direct test of significant additive differences in the logarithmic wage equations in the public and private sectors (table 3). The coefficient on public sector status is insignificantly different from zero in both union and nonunion sectors. This holds for both corrected and uncorrected coefficients, though in the latter case a sizable positive point estimate for the differential is significantly different from zero at the 10% level. Thus the direct estimates provide little evidence of significant positive public sector differentials in either union or nonunion sectors. This is reflected in table 7, where the coefficients of tables 2 and 3 are used to compute public sector differentials. Using the coefficients from table 3, all the public sector differentials ((k) are negative except for a small positive differential for unionized females. Without the selectivity correction in the wage equations, the public sector differentials are negative for unionized and nonunionized males and positive for females. The disaggregated wage equations of table 2 may also be used to compute public-private sector differentials (ig). However, as noted in the previous section, the disaggregation results in small sample sizes for some of the subsamples, particularly nonunion-public sector workers. Thus, the disaggregated results must be treated with special caution. In computing the public sector differentials implied by the wage equations of This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms 124 Robinson/Tomes table 2, the level of union organization was set at the same level in both public and private sectors. As noted above, the level of organization is 67.8% for all public sector workers and hence is omitted from the public sector wage equation. Its effect is captured in the constant term. In order to hold the level of organization across public and private sectors constant, the private sector wage equation, which explicitly includes the percentage of organized workers, was evaluated at a level of organization of 67.8%. Using the corrected coefficients, the disaggregated wage equations yield public-private sector differentials in the union sector that are similar to those obtained from the pooled sample. In the nonunion sample there is some divergence: the disaggregated wage equations show positive differentials for both males and females, whereas using the pooled sample equations they are both negative. However, the disaggregated sample sizes are small, hence the disaggregated results are subject to potentially large errors. In addition, significance tests on additive public sector effects in the union and nonunion wage equations showed no significant public sector differential. The evidence against a public sector differential was also strengthened by the instrumental variables analysis of equation (6). The coefficient on public sector status, irrespective of whether union status was treated as exogenous or endogenous, was always insignificantly different from zero. Finally, some estimates of the potential overestimate of public sector differentials from omitting union controls may be made. First, the effect of not setting the level of organization the same in both public and private sectors when the disaggregated equations are used is substantial. For average unionized males a negative public-private sector differential of -9.34% becomes a positive 6.42%. For average unionized females a negative differential of -2.24% becomes a positive 14.75%. Second, if union membership itself is not controlled for, there is a marked increase in the estimated public-private sector differential. For example, using the pooled sample, we estimated that unionized males earn 7.49% less in the public sector than in the private sector and nonunionized males 22.24% less. However, when the estimated wage rates are weighted by the proportions of union and nonunion members in each sector, the differential becomes zero. If females are also included in the calculation, even though three out of four subgroups have negative public sector differentials, the average public-private sector differential without controlling for union status is positive, approximately 5%. This suggests that apparent public sector rents found in the absence of controls for union status (e.g., Gunderson 1979a) may in fact be largely union differentials. IV. Conclusions Large estimated union differentials for hourly paid workers were obtained in Section II, controlling for union status. There was considerable This content downloaded from 147.251.55.15 on Thu, 29 Mar 2018 09:06:54 UTC All use subject to http://about.jstor.org/terms Union Wage Differentials 125 evidence of positive selection into the union sector, especially for private sector workers. Union status appears to be strongly affected by the expected wage gain from joining the unionized sector. There was some evidence of larger union gains in the public sector than in the private sector from the pooled sample estimates, but this was not replicated in the disaggregated estimates. Estimates of public-private sector wage differentials were presented in Section III. Typically these were negative, though disaggregated results suggested a positive differential for nonunionized workers, particularly females. 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