Union Membership, Union Organization and the Dispersion of WagesAuthor(s): Dale Belman and John S. HeywoodSource: The Review of Economics and Statistics, Vol. 72, No. 1 (Feb., 1990), pp. 148-153Published by: The MIT PressStable URL: http://www.jstor.org/stable/2109751Accessed: 12/03/2009 10:28

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148 THE REVIEW OF ECONOMICS AND STATISTICS

UNION MEMBERSHIP, UNION ORGANIZATION AND THE DISPERSION OF WAGES

Dale Belman and John S. Heywood*

A bstract-A variance components model explains wage disper- sion with a specific version of generalized least squares. The estimation preserves individual data while examining the in- fluence of union penetration on dispersion in both the union and nonunion sectors. Controlling for both individual and industry characteristics and for the endogeneity of wages, union penetration correlates strongly with reduced dispersion in the union sector but not in the nonunion sector. A decompo- sition reveals the relative importance of the influences of union penetration and of union membership.

I. Introduction

Freeman (1980 and 1982) suggests that a primary objective of trade unions is to reduce wage dispersion through the use of standard rates. He demonstrates that the dispersion of log wages is much smaller for union members than for nonmembers even after controlling for major differences in human capital and personal characteristics. Kahn and Curme (1987) provide related information using a different approach. Examining the union and nonunion sectors separately, they use the variance in log wages for industry and occupation cells as the dependent variable in regressions which include, along with other controls, the percentage of the indus- try's workers who are unionized. They find that the percent organized fails to influence the variance across cells in the union sector but correlates with lower wage dispersion in the nonunion sector. Kahn and Curme claim the latter result flows from union wage spillover which disproportionately increases the wages of lower paid nonunion workers.

Clearly, the total influence of unions on dispersion includes both the effect of membership and the effect of the percentage organized. Using an individual metric of dispersion we develop a methodology which captures both effects and retains the individual data lost by Kahn and Curme. Further, we protect against bias in our results through inclusion of relevant industry vari- ables and adjusting for industry specific random effects.

We find that union members have smaller wage dis- persion than their nonunion counterparts. In addition, we demonstrate that percent organized reduces disper-

sion in the union sector while having little or no effect in the nonunion sector. Moreover, the majority of the gap in dispersion between members and nonmembers can be attributed to the influence of union organization. These findings persist after adding industry characteris- tics to the individual controls and accounting for the endogeneity of wages.

II. Percent Organized and Dispersion

Kahn and Curme present a model in which nonunion firms tilt threat-induced wage- increases toward low-wage workers thereby reducing nonunion wage dispersion. This tilt emerges as optimal because low-wage workers would be most advantaged by unionization. Although the specific model is based on restrictive assumptions, such as low-wage workers being at least half the work force and monotonic probability derivatives, the basic logic seems open to question. Lewis (1986) argues that correlations between percent organized and wages may evidence little beyond omitted variable bias.' If this argument is correct, assuming that nonunion employers increase wages to discourage unionization is unfounded. Yet, it is this assumption which ties unions to nonunion wage dispersion.

Even if one accepts the attempt to discourage union- ization through more generous wage policies, dispersion need not narrow. Incentive schemes, such as piece-rates or tournaments, can simultaneously increase both the utility of nonunion workers and wage dispersion. As each worker perceives a chance of receiving incentive payments, the average utility level increases, discourag- ing unionization. On the other hand, observed wage dispersion could increase.

More generally, one might expect percent organized to reduce wage dispersion in the union sector rather than the nonunion. Unions in weakly unionized indus- tries may have difficulty altering wage dispersion for much the same reason they have difficulty increasing wage levels. By increasing the wage level, the union puts its firm at a competitive disadvantage relative to its nonunion rivals. Reducing dispersion may create a com- petitive disadvantage for a unionized firm in much the same way. The firm may be forced to alter its mix of labor "types" (education, skills and so on) in an ineffi- Received for publication November 8, 1988. Revision ac-

cepted for publication April 19, 1989. * University of Wisconsin-Milwaukee. The authors thank Barry Hirsch, John Gross, Mathew

Higgins and Paula Voos for detailed comments on earlier drafts.

1 See Heywood (1989) for evidence on the portion of the return to percent organized actually attributable to differences in employment security.

Copyright (?) 1990

NOTES 149

cient way compared to its nonunion rivals. Thus, per- cent organized may partially reflect managerial resis- tance to union demands. Firms will more likely yield to union demands, including standard rates, when their rivals face similar demands.

As theory does not provide a convincing explanation of the relationship between unions and wage dispersion, much less a clear specification of the dispersion equa- tion, choice of estimation strategies is particularly im- portant. As suggested by Lewis, wages and wage disper- sion may be driven by industry factors other than percent unionized. Accurate measures of the influence of percent unionized thus require the inclusion of other industry variables and accounting for common error structures within industries, an inevitable result of omit- ting some industry variables.

Aggregation presents a related estimation issue. Use of the wage variance within occupation and industry cells (e.g., service workers in the steel industry) presents an intermediate degree of aggregation between individ- ual and industry level observations. Moulton (1985) demonstrates that disaggregate specifications may exag- gerate the significance of aggregate variables if common industry error components exist. On the other hand, aggregation may alter relative variances and change the weights of industry variables such as percent organized. This seems particularly likely when observations are eliminated because their cell count does not permit sensible inference.2 Thus, estimates using industry and occupation cells seem potentially subject to aggregation difficulties.

Individual observations can be used to retain the full data set, the original weights of aggregated variables, and maximum efficiency. At the same time, industry error components must be accounted for as highlighted by Moulton and this must be done in a manner which isolates the effect of percent organized which Freeman's method did not. Finally, one should be able to examine the interaction of the influence of percent organized with the influence of membership per se.

III. Empirical Strategy

Within the union and nonunion sectors one can com- pute a variety of individual dispersion metrics. Such metrics include the absolute deviation in log wage from the mean log wage of the sector, the squared deviation in log wage from the mean log wage, and the absolute deviation in wage from the mean wage, or from the

median wage.3 All four measures can be created for each observation and used as dependent variables.

In what follows, we explain the absolute deviation in log wage for the private nonagricultural work force sampled in the May 1983 Current Population Survey. This survey includes a rich set of personal controls to which we add relevant industry variables. Following the standard earnings equation, we create measures of the absolute deviation in education, in experience, and in tenure. To these we add regional dummies, occupational dummies, dummies for gender, race, marital status, residency in an SMSA, part-time employment and plant size. We also generate three industry level variables: the percentage of the three-digit industry which is unionized in 1981 (Kokkelenberg and Sockell, 1985), an employ- ment weighted four-firm concentration ratio for the industry, and the capital to labor ratio in the industry.4 We also add a fourth industry measure, the predicted average log wage.5 As Hirsch (1982) points out, high average wages may be correlated with both the percent organized and the degree of wage dispersion. The in- strumental variable avoids possible bias introduced by using the actual industry average.

We estimate a variance components model in which individual variables capture the variance in dispersion within industries, while industry variables capture the variance between industries. In particular, our model takes the form

DISPij= aXj + b'Zj + (u+w), (1)

where there are J industries and the variables are:

DISPij = the measure of individual wage dispersion Xij= a vector of individual characteristics for

individual i in industry j Z = a vector of industry characteristics shared

by all individuals in industry j ui = the individual component in the error term Wj = the industry component in the error term

Although the industry component in the error will not bias OLS coefficient estimates, hypothesis tests will be invalid because estimated standard errors are inconsis- tent. Consistent estimates of standard errors and effi- cient estimates of coefficients can be obtained by adapt-

2 Kahn and Curme retain only 60% of their nonunion and 28% of their union cells after eliminating all those with less than ten observations.

3We estimate our model using each of these as dependent variables. The estimations not presented are available from the authors.

4 The latter variables are generated from four-digit SIC in- dustries as presented in the Census of Manufactures and then bridged to the three-digit CPS classifications. Such variables are traditionally available only for manufacturing forcing us to limit our sample to these industries.

5 We estimate an individual level wage equation and then average the predicted values by industry.

150 THE REVIEW OF ECONOMICS AND STATISTICS

ing the generalized least squares (GLS) procedure pro- posed by Mundlak (1978).

Under the assumptions that the u's are iid across individuals, the w's are iid across industries, and the u's and w's are independent, the variance matrix for the errors is block diagonal with each block correspond- ing to an industry:

j= aTj + ggI tj (2)

where Tj is the number of individuals in industry j, tj is a (Tj X 1) vector of ones, q2 is the individual variance component, and a,d2 is the industry component. The inverse of the variance matrix, V- 1, is also block diago- nal with the jth industry's block taking the form:

Vj =i(d; f\ ITJ -

2 j(3)

We calculate q2 and a2 from the residuals of an ordi- nary least squares version of equation (1), thereby ob- taining Vj-i for the J industries. 6 Forming V1, we get GLS coefficient estimates,

( [ XIZ]'V-1[ XIZ]) 1

[ XIZ]'V-'DISP,

and their variance matrix, ([XIZI'V '[X Z]f- .

We estimate separate dispersion equations for the union and nonunion sector. The GLS coefficient on percent organized estimates the influence of organiza- tion while the difference in predicted values between sectors helps estimate the influence of membership. As percent organized is in each equation the two influences may be highly interactive.

IV. Empirical Results

Table 1 presents the results explaining the absolute deviation in log wage. The first and fourth columns use

percent organized as the only industry variable, the second and fifth columns add the concentration ratio and capital to labor ratio, while the third and sixth columns also add the predicted average log wage. The most immediate result is the strong influence of union organization in the union sector and the near absence of influence in the nonunion sector. Holding all else con- stant, moving union members from an unorganized industry to a fully organized industry reduces dispersion in the log of wages by 0.19. In the nonunion sector percent organized starts out significant and positive, but reduces to insignificance as the other industry variables are added.7

The general pattern of results differs between the two sectors. While higher average industry wages correlate with lower dispersion in both sectors, other variables play a role only for nonunion workers. Indeed, the nonunion estimations appear more robust with many more significant variables. These include the education and experience deviations, occupational dummies, race, marital status, plant size and industrial concentration. Only gender loses significance in the nonunion sector. Note that failure to include a part-time variable, or limit the sample to only full-time, could result in omit- ted variable bias. Union members are disproportion- ately full-time, suggesting that excluding part-time might yield a spurious negative correlation between percent organized and dispersion.8

As these results differ substantially from those of Kahn and Curme, we made an effort to attribute the differences to either our estimation methodology or our sample. We replicated their approach with mixed find- ings. For example, the nonunion education measure, emerges positive and significant in Kahn and Curme, in our replication and in our current estimations. The average ln wage measure was positive in Kahn and Curme but negative in both our replication and our current estimations highlighting the difference in data sets. In contrast, the nonunion experience measure was positive in both Kahn and Curme and our replication but negative in our current estimations highlighting the difference in methodologies. Other variables could not be classified so easily. The union plant variable was negative in Kahn and Curme, insignificant in our repli- cation and positive in our current estimations. Similarly, Kahn and Curme found a negative coefficient for per- cent organized in the nonunion sector while our replica- tion presented insignificance in both sectors and our current estimations emerge with a negative coefficient in

6 We obtain the variance components by noting that, within industry j, E(u. + w.) = w;. The OLS residuals within each industry are summed and divided by the number of observa- tions in the industry, to obtain an estimate of wj. The squared value of w; is summed across the j industries and divided by the number of industries less one to provide the estimate of a2.

By subtracting each industry's wj from the OLS residual, we obtain estimates of ui, which are squared, summed across all industries, and divided by the number of observations less the number of coefficients and industries, to provide an estimate of

au2, the individual component of variance. Industries with fewer than six observations were excluded from the sample to im- prove the accuracy of our estimates of the variance compo- nents. Note that such a procedure still retains a larger share of the data than the elimination of all small industry occupation cells.

7 Analogous estimations using the other dependent variables reveal virtually identical results on this key point.

8 There is no mention in Kahn and Curme of their treatment of part-time workers. Note that attempts to use an instrumen- tal measure for percent unionized did not substantially alter the results of table 1.

NOTES 151

TABLE 1.-DETERMINANTS OF THE DEVIATION IN LOG WAGES

Union Nonunion

1 2 3 4 5 6

Constant 0.4535 0.4634 0.9368 0.3320 0.3050 0.7182 (9.230) (8.791) (6.091) (8.940) (7.204) (6.896)

white -0.0069 -0.0068 -0.0049 -0.0427 -0.0447 -0.0411 (0.372) (0.363) (0.259) (2.402) (2.596) (2.387)

male - 0.0443 - 0.0447 - 0.0391 0.0109 0.0103 0.0141 (2.962) (2.982) (2.598) (0.909) (0.860) (1.175)

married -0.0103 -0.0105 -0.0105 -0.0313 -0.0312 -0.329 (0.724) (0.742) (0.747) (2.793) (2.788) (2.937)

Ed Dev 0.0033 0.0033 0.0032 0.0159 0.0159 0.0152 (0.883) (0.872) (0.853) (5.913) (5.914) (5.669)

Exp Dev - 0.0015 - 0.0015 - 0.0016 - 0.0034 - 0.0034 - 0.0034 (1.602) (1.602) (1.690) (4.283) (4.287) (4.357)

Ten Dev 0.0025 0.0025 0.0025 0.0064 0.0064 0.0064 (2.346) (2.339) (2.333) (6.479) (6.463) (6.474)

Part-time 0.1708 0.1706 0.1687 0.2014 0.2025 0.2008 (3.883) (3.871) (3.843) (8.663) (8.708) (8.644)

NE -0.0357 -0.0360 -0.0372 -0.0194 -0.0194 -0.0220 (1.601) (1.636) (1.676) (1.174) (1.174) (1.337)

NC -0.0344 -0.0347 -0.0331 -0.0133 -0.0127 -0.0153 (1.600) (1.610) (1.547) (0.816) (0.837) (0.917)

South 0.0001 - 0.0004 - 0.0009 0.0196 0.0197 0.0147 (0.004) (0.016) (0.042) (1.219) (1.233) (0.917)

SMSA 0.0013 0.0016 0.0036 0.0080 0.0078 0.0112 (0.099) (0.122) (0.272) (0.709) (0.691) (0.984)

Large - 0.0166 -0.0154 - 0.0142 0.0301 0.0274 0.0309 Plant (0.959) (0.882) (0.816) (2.192) (1.968) (2.221)

Medium - 0.0107 - 0.0106 - 0.0107 - 0.0097 - 0.0102 - 0.0101 Plant (0.653) (0.639) (0.647) (0.796) (0.838) (0.826)

Manager 0.1219 0.1217 0.1285 0.0336 0.0330 0.0386 (2.617) (2.610) (2.763) (1.927) (1.889) (2.209)

Prof 0.1049 0.1051 0.1104 0.1031 0.1012 0.1093 (2.617) (2.671) (2.818) (5.294) (5.183) (5.579)

Tech 0.0626 0.0629 0.0657 0.0376 0.0354 0.0426 (1.551) (1.565) (1.643) (1.434) (1.351) (1.624)

Sales -0.0388 -0.0390 -0.0382 0.0146 0.0136 0.0214 (0.603) (0.640) (0.595) (0.530) (0.493) (0.776)

Clerical - 0.0268 - 0.0269 - 0.0232 - 0.0970 - 0.0982 - 0.0942 (1.155) (1.084) (1.092) (5.963) (6.032) (5.786)

Protect 0.1241 0.1257 0.1430 -0.0184 -0.0186 -0.0167 (1.079) (1.159) (1.239) (0.206) (0.209) (0.187)

Service 0.0025 0.0029 0.0003 - 0.0099 - 0.0116 - 0.0137 (0.057) (0.067) (0.007) (0.198 (0.234) (0.277)

Craft 0.0215 0.0216 0.231 - 0.032i - 0.0334 - 0.0313 (1.503) (1.506) (1.614) (2.157) (2.189) (2.052)

Percent - 0.0025 - 0.0024 - 0.0019 0.0013 0.0009 0.0005 Organized (2.769) (2.585) (2.138) (1.945) (1.688) (1.336)

Conc Ratio - 0.0005 0.0005 0.0007 0.0027 (0.523) (0.602) (1.061) (3.265)

K/L Ratio 0.00001 0.00005 0.00001 0.00001 (0.367) (1.711) (1.397) (2.439)

Ave Log Wage -0.2589 -0.2584 (Instrument) (3.265) (4.342)

N 1189 1189 1189 2553 2553 2553

Note: t-statistics are in parentheses.

152 THE REVIEW OF ECONOMICS AND STATISTICS

TABLE 2.- DECOMPOSING THE DIFFERENCE IN DISPERSION BETWEEN SECTORS

Differences from Differences from Union Membership Union Penetration Total

Differences from characteristics 0.0081 0.0247 0.0328

(7.6%) (23.0%) (30.6%) Differences from

coefficients 0.0047 0.0696 0.0743 (4.4%) (65.0%) (69.4%)

Total 0.0128 0.0943 0.1071 (12.0%) (88.0%) (100.0%)

the union sector. Such findings suggest that the differ- ences in results are partially a function of data and partially a function of testing methodology.9

The remainder of this section isolates the separate influences of union membership and penetration through the use of a modified Oaxaca (1973) decomposition. The average absolute dispersion in log wage for the nonunion sector is 0.4057 while that for the union sector is 0.2986. This difference of 0.1071 is decomposed into a portion accounted for by membership and a portion accounted for by penetration. In turn, each portion is further decomposed into that part resulting from differences in coefficients and from differences in characteristics.

To analyze the membership influence we hold percent organized at its nonunion mean, 31.1, and its coefficient at the nonunion value of 0.0004.10 We then compute the average predicted dispersion for the union sample in both the nonunion and union equations. These esti- mates are 0.3976 and 0.3929, respectively. That is 0.0081 of the total difference flows from differences in sector characteristics while another 0.0047 flows from differ- ences in sector coefficients other than that on percent organized. Next we allow the union sector coefficient to take on its true coefficient of - 0.0019 but again hold percent organized in both sectors to its nonunion mean. The predicted union dispersion is 0.3233. Finally, allow- ing the percent organized in the union sector to take on its true mean, 41.4, the actual union dispersion of 0.2986 again emerges. Thus, 0.0696 of the difference emerges from the difference in the coefficient on the percent organized, while 0.0247 of the difference results from the difference in the percent organized between the two sectors.

Table 2 presents the estimates and highlights the importance of the difference in the coefficient on per-

cent organized between sectors. Nearly two-thirds of the entire difference in dispersion is accounted for by the difference in this one coefficient. Note that estimates of the dispersion equations which failed to include percent organized would yield the same mean dispersion mea- sures for each sector. While this would allow decompo- sition into the difference attributable to characteristics and to coefficients, it would inappropriately attribute to membership the reduction actually associated with the extent of organization. Despite different methodology, Freeman (1980) would seem to have made this attribu- tion by not including percent organized in his estima- tions.

VI. Conclusions

This paper presents a new testing methodology for simultaneously examining the effects of union member- ship and the extent of union organization on wage dispersion. By using individual metrics of dispersion, the methodology retains individual data and credibly accounts for industry level effects. The estimations ac- complish this by including industry level variables, in- cluding an instrumental measure of average industry wage, and by adopting a specific GLS technique which allows for common error components within industries.

The percent organized emerges as a significant partial correlate with dispersion in the union sector but not in the nonunion sector, the opposite of previous work. Moreover, the influence of percent organized accounts for nearly two-thirds of the gap in dispersion between the nonunion and union sectors. The importance of percent organized holds across metrics and across varia- tions in specification. Thus, previous work attributing the entire gap in dispersion to union membership have overestimated that influence, suggesting that future esti- mations should incorporate the extent of unionization. 9 The full replication results are available upon request. We

thank Lawrence Kahn for help in performing the replication. 10 This latter value is taken from column 6 of table 1. The

somewhat high mean value results, in large part, from our focus on manufacturing. Note that an alternative method might have been to hold percent organized at zero in both equations but this method could be unreliable as zero is outside the range of generally observed values.

REFERENCES

Freeman, Richard B., " Unionism and the Dispersion of Wages," Industrial and Labor Relations Review 34 (Oct. 1980), 3-23.

NOTES 153

_ , "Union Wage Practices and Wage Dispersion Within Establishments," Industrial and Labor Relations Review 36 (Oct. 1982), 3-21.

Heywood, John, "Do Union Members Receive Compensating Differentials? The Case of Employment Security," Jour- nal of Labor Research 10 (Summer 1989), 271-284.

Hirsch, Barry, "The Interindustry Structure of Unionism, Earnings and Earnings Dispersion," Industrial and La- bor Relations Review 36 (Oct. 1982), 22-39.

Kahn, Lawrence M., and Michael Curme, "Unions and Nonunion Wage Dispersion," this REVIEW 69 (Nov. 1987), 600-607.

Kokkelenberg, Edward, and Donna Sockell, "Union Member- ship in the United States, 1973-1982," Industrial and Labor Relations Review 38 (July 1985), 497-543.

Lewis, H. Gregg, Union Relative Wage Effects: A Survey (Chicago: University of Chicago Press, 1986).

Moulton, Brent, "Random Group, Effects and the Precision of Regression Estimates," U.S. Bureau of Labor Statistics Working Paper, Nov. 1985.

Mundlak, Yair, "On the Pooling of Time Series and Cross Section Data," Econometrica 46 (1978), 69-85.

Oaxaca, Ronald, "Male-Female Wage Differentials in Urban Labor Markets," International Economic Review 16 (Oct. 1973), 693-709.

QUANTITY AGGREGATION IN CONSUMER DEMAND ANALYSIS WHEN PHYSICAL QUANTITIES ARE OBSERVED

Julie A. Nelson* Abstract-A method for estimating price and income elastici- ties from cross section data devised by Deaton (1986, 1987, 1988) makes implicit use of the Hicks' composite commodity theorem. Recognition of this fact allows theoretically rigorous definition of aggregate composite quantities. A comparison of elasticities of the Hicks' composite with elasticities of simple physical quantity measures for the Ivory Coast and the United States demonstrates that use of physical quantity measures can be severely misleading when commodity heterogeneity is sub- stantial.

In a recent series of papers, Deaton (1986, 1987, 1988) has addressed some of the theoretical and econo- metric problems which can arise in the estimation of price and income elasticities when the researcher is given data on expenditures and physical quantities of purchases of non-homogenous commodities. This short paper extends Deaton's analysis to show that implicit in his model is a form of aggregation which does not depend, as his model does, on the researcher choosing a particular characteristic of the good by which to mea- sure quantity, and which is more in keeping with the more common type of demand analysis done using data on expenditures and prices. Deaton's results from the Ivory Coast are extended to the new case, and com- pared to results derived using the same methodology for the United States.

I. Theoretical Issues

Deaton aggregates quantities of food items by sum- ming the reported number of kilos purchased in each food category, though he leaves his formulation general

enough "that aggregation could be done with respect to other characteristics, for example, calories" (1988, p. 421). An obvious problem with this method, if the goods in the group are heterogeneous, is that there exists not one elasticity of physical quantity, but possi- bly as many physical quantity elasticities as there are dimensions in which to measure the good. While one or another of these might be of primary interest to a particular researcher, there exists no unique number that is "the" elasticity of demand for the good, as the concept is generally understood. Consider, for example, the different income elasticities one might get from measuring ice cream demand by volume versus by weight. If premium brands weigh more per unit of volume than cheap brands, income elasticities could very well be positive by weight while at the same time negative according to volume.

In contrast, researchers using the more commonly available data on expenditures and prices (rather than expenditures and physical quantities) appeal, at least implicitly, to standard results of aggregation theory in order to come up with a single, well-defined price elas- ticity for each commodity. These same theoretical re- sults are just as applicable (or perhaps, inapplicable, if the assumptions do not hold) in the case where physical quantity data are available but independent price data are not. As Deaton makes the assumption in his model that the relative price structure is fixed within each commodity group and geographical cluster of house- holds (1988, pp. 421-22), the application of Hicks' composite commodity theorem provides a theoretically rigorous means of obtaining a single, well-defined price elasticity of demand using his estimation methodology.

In Deaton's notation, q is the vector of physical quantities (by weight) of purchases within the group, Q is the unweighted sum of physical quantities, p* is the vector of fixed relative prices (by weight) of the goods

Received for publication December 23, 1987. Revision ac- cepted for publication April 27, 1989.

* University of California, Davis. This paper was written while the author was employed by the

Division of Price and Index Number Research, United States Bureau of Labor Statistics (BLS). Ti.e views expressed herein are the author's and do not represent an official position of the BLS or the views of other BLS staff members.

Copyright C) 1990