The Board of Regents of the University of Wisconsin System
Nominal and Real Union Wage Differentials and the Effects of Industry and SMSA Density:
1973-83
Author(s): Barry T. Hirsch and John L. Neufeld
Reviewed work(s):
Source: The Journal of Human Resources, Vol. 22, No. 1 (Winter, 1987), pp. 138-148
Published by: University of Wisconsin Press
Stable URL: http://www.jstor.org/stable/145872 .
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Nominal and Real Union Wage Differentials and
the Effects of Industry and SMSA Density:
1973-83
I. Introduction
Estimation of union-nonunion relative wage differentials has
for some time received considerable attention from labor economists. Lewis
(1986) has recently surveyed about 200 empirical studies providing empirical analysis of data through 1979. In this paper, we provide estimates of
nominal and real union-nonunion wage differentials for the period 1973-83,
based on separate samples of male production workers in manufacturing,
production workers in nonmanufacturing, and nonproduction workers
economy wide.
The purpose of this study is threefold. First, systematic comparison of
nominal versus real wage differentials allows us to evaluate Lewis's conclusion, based on a limited number of studies, that there is no significant
difference between these measures. Second, we are able to provide estimates of the union-nonunion differential over an eleven year period, including several sample years since Lewis ended his survey. Finally, we provide
estimates of the effects of both industry and SMSA density on the union
differential and the wages of union and nonunion workers.
II. Estimation and Data
In order to obtain estimates of the union-nonunion wage
differential, micro log wage functions are specified for union and nonunion
workers. Letting i index individual workers, k a worker's 3-digit industry, m
a worker's SMSA, and superscripts u and n union and nonunion status,
respectively, the following equations are estimated by OLS:
(1)
ln(w)' = Ox"+ SEIP"X + UPik + 8UPim+ e'
(2)
ln(w)i = an + SX?
+ ^"P + 8p
+e
where w is the wage, X is a vector of earnings-related individual characterisThe authorsacknowledgethe helpfulcommentsof two anonymousreferees.
[SubmittedAugust 1985;acceptedJuly 1986]
THE JOURNAL
OF HUMAN
RESOURCES
? XXII
* 1
Communications
tics, P is union density, and e" and en are error terms assumed to be
uncorrelated with zero means and constant variances.'
The logarithmic union-nonunion wage differential (or wage gap), d, is
calculated by:
(3)
d = (ou -
") +
(
-
n)+
(U
- yn)Pk
+ (u
-
)Pm.
where the means of X, Pk, and Pm are all-worker means (hence, d is a
weighted average of log differentials calculated using union and nonunion
means). The percentage differential, D, is most easily approximated by:
(4) D = [exp(d) - 1]100.
More precise estimation methods are provided in Kennedy (1981) and Giles
(1982). Below, all results are presented as log differentials.
The primary data used in this study come from the May 1973-81 and 1983
Current Population Survey (CPS) tapes. All employed nonfarm nonschool
males between the ages of 18 and 64 residing in 29 of the largest 30 SMSAs
are included.2 Union density, defined here as the percentage of eligible
workers who are union members, is available for three-digit Census industries and SMSAs in Kokkelenberg and Sockell (1985).3 In order to obtain
real wage estimates, nominal wages (usual weekly earnings divided by usual
hours worked per week) are deflated by BLS intermediate budget figures
once provided annually for large SMSAs (Census Bureau).4 The vector X
includes years of schooling, experience (age - schooling - 5), experience
1. As is well known, OLS is not without problems. Receiving the most attention in the
literature has been the potential bias resulting because of the simultaneous determination of
union status and wages and, relatedly, selectivity bias resulting from unobserved differences
between union and nonunion workers with identical measured characteristics. Lewis (1986)
provides an analysis of methods intended to address these problems (e.g., inclusion of a
selectivity variable in the wage equations and the use of fixed-effects models with panel data).
Because alternative methods also introduce potentially serious problems, OLS is used here.
This helps avoid entangling the effects of cost-of-living or union density adjustments with those
from use of alternative estimation procedures.
2. There was no public use 1982 survey. Sample sizes are reduced after 1978 because all
rotations were not asked their usual weekly earnings. CPS coding of the SMSAs is based on
1970 Census population counts. Miami is excluded due to insufficient cost-of-living data.
3. Kokkelenberg and Sockell (1985) provide union data based on the 1973-81 May CPS (the
CPS union question did change during this period; see Footnote 6). Density data for SMSAs are
provided yearly while for industries, data are presented as three-year moving averages. Hence
our 1973 and 1974 regressions include industry density for 1973-75, regressions for 1980 on
include the 1979-81 industry density measures, and the 1983 regressions include the 1981
SMSA density measure. Measurement error associated with this imperfect matching is probably minor given the year-to-year stability in relative interindustry and interarea unionization.
4. Such figures are no longer provided by BLS. Our 1983 budget figures were generated by
inflating prior year budget figures by SMSA-specific consumer price indices (U.S. Bureau of the
Census).
139
140 The Journalof Human Resources
squared, and dummies for race, marital status, veteran status, region,
samples).
1-digitoccupation,and 1-digitindustry(in the nonmanufacturing
III. Nominal versus Real Wage Differentials
by Year
As noted by Lewis(1986, 105), the use of nominalratherthan
real wage rates might lead to an upwardbias in wage gap estimatessince
unionworkersare more likelyto residein highercost-of-livingareas.Based
on unpublishedresultsextractedfrom four studies, however, Lewis tentativelyconcludesthat adjustmentsfor cost of livinghave little effect on wage
differentialestimates.We firstexaminethe potentialfor bias in unionwage
differentialestimatesby comparingdifferencesbetween nominaland real
wage rates for union and nonunionworkersover the 1973-83 period. As
hypothesizedby Lewis, we find a potentialfor bias. Adjustingfor cost-oflivingdifferencesreducesunionwagesby an average1.15percentrelativeto
nonunionwages.
Table 1 presentsestimates of union-nonunionlog wage differentialsby
yearfor the threesubsamplesof maleworkers.As foundin previousstudies,
the union wage effect for productionworkersis smallerin manufacturing
than in nonmanufacturing,while estimatedunionwage effects for nonproduction workersare close to zero (see Antos 1983).
The average (unweighted)differencebetween the nominaland real differential over the 1973-83 period, d(nom) - d(real), is presentedin the
next to last row of Table 1. Among productionworkersin manufacturing
(the most frequentlystudiedgroupin the empiricalliterature),nominaland
real differentialsare virtuallyidentical, the averagedifferencebeing less
than a tenth of a percent. However, amongproductionworkersoutside of
manufacturing,estimates of nominaldifferentialsare about 1 percentage
point higherthan estimatesof real differentials.While a 1 percentagepoint
bias is not trivial,it is less thanthe bias attributedto the exclusionof fringe
benefits (Freeman 1981), work conditions (Duncan and Stafford 1980),
union dues (Raisian 1983), selectivity,and other factors(for a survey, see
Lewis 1986). Among nonproductionworkers, no evidence is found of a
union-nonunionwage differential;hence, values of d(nom) - d(real) for
this grouphaveless meaning.The bottomline of Table 1 presentsd(nom) d(real) calculatedfrom regressionsexcludingthe regionalvariables,which
to some extent proxycost-of-livingdifferences.Even with the exclusionof
these controlvariables,differencesbetween nominaland real union wage
gaps are small on average (complete results are availableon request).
On the basisof the resultspresentedin Table 1, it appearsfairto conclude
that no significantportionof the union-nonuniondifferentialconstitutesa
Communications
compensating differential for higher living costs. It likewise follows that no
significant bias has been introduced in previous studies by ignoring cost-ofliving differences. For most research efforts in this area, the benefits from
considering cost-of-living differences are likely to be less than the costs of
limiting one's sample to large SMSAs (plus the costs from introducing
additional measurement error associated with the cost-of-living indices).5
Indeed, it should be noted that union wage gaps estimated for workers in
SMSAs are lower than corresponding economy-wide wage gaps (Lewis
1986, 134-36).
Our results also provide evidence on changes over time in the unionnonunion wage differential, using a common methodology, specification,
and data source.6 The far right columns of Table 1 report the full-sample
weighted averages of the nominal and real differentials. Similar to results
reported by Lewis (1986, 179, 186), we find relatively stable wage effects
from 1973 through 1975. However, we find a more marked upward shift than
reported in Lewis for the 1976-78 period. As in the three studies cited by
Lewis, we find a sharp drop in the 1979 estimated gap. Our post-1979 results
show considerable year-to-year variability, with somewhat higher production-worker gap estimates for 1980 and 1983 than in 1979 and 1981. It
appears fair to conclude that the upward trend occurring in the union
differential in the late seventies may have been less marked than that
estimated by some (e.g., Johnson 1984, Linneman and Wachter 1986), and
it was not maintained in the early eighties.
IV. Union Density and the Wages of
Union and Nonunion Workers
Lewis (1986) has argued forcefully that much of the empirical
literature measuring union relative wage effects entangles to some degree
the effects of individual union status and of union density. In order to
separate these effects, variables measuring union density in workers' threedigit industry group and SMSA are included in Equations (1) and (2).
Because inclusion of density variables in wage equations has only recently
5. We have no reason to believe that these results, based on large SMSAs, cannot be generalized.
6. The union variable does change in definition over the period. The 1973-75 surveys asked,
"Does ... belong to a labor union?" The 1976-78 surveys added to the end, ". . . or employee
association." The 1979-81 surveys added, ". .. or employee association similar to a union."
The 1983 survey asked, "Is . . . covered by a union or employee association contract?" These
changes in definition qualify any inferences we make regarding intertemporal changes in the
union wage gap.
141
Table 1
Nominal and Real Union-Nonunion Log Wage Differentials: 1973-83
Production Workers
Year
1973
1974
1975
Manufacturing
nominal
real
0.0770
0.0775
663]
[1107;
0.0970
0.0978
[1055; 625]
0.0784
0.0746
[992; 638]
0.1026
1976
0.1038
1977
[870; 626]
0.1229
0.1220
[956; 660]
Nonmanufacturing
nominal
real
Nonproduction
Workers
nominal
real
0.1881
0.1819
[1336; 1391]
-0.0192
-0.0258
0.2262
0.2350
[1214; 1228]
0.1993
0.1917
[1177; 1325]
0.2333
0.2419
[1128; 1267]
0.2950
0.2826
[1257; 1451]
-0.0337
-0.0427
[599; 2797]
0.0060
-0.0045
[599; 2994]
0.0003
-0.0062
[573; 2774]
0.0064
-0.0001
[618; 2876]
[662; 2806]
1978
1979
1980
1981
1983
1973-83a
0.1330
0.1339
[819; 557]
0.0835
0.0837
[540; 358]
0.1037
0.0999
[250; 220]
0.0549
0.0590
[236; 233]
0.1133
0.1152
[281; 243]
- 0.0005
0.2697
0.2577
[1137; 1333]
0.1907
0.1835
[677; 787]
0.2237
0.2142
[371; 485]
0.1457
0.1304
[325; 483]
0.2045
0.1946
[300; 381]
0.0097
d(nom) - d(real)
1973-83b
d(nom) - d(real)
0.0005
0.0074
0.0008
-0.000
[581; 2771]
-0.0515
-0.057
[408; 1654]
-0.0238
-0.031
[206; 961]
0.0097
0.00
[192; 949]
-0.0225
-0.024
[342; 11471
0.0065
0.0106
Note: Samplesizes for union and nonunionworkers,respectively,are in brackets.
a. Unweightedaveragefor 1973-83, calculatedfrom values in the table.
b. Unweightedaveragefor 1973-83, calculatedfrom differentialsestimatedwith regressions
excludingregionaldu
Table 2
Industry and SMSA Union Density Coefficients from Union and Nonunion Real Wage Equa
EquationDensity
Variable
1973
1974
1975
Production workers: manufacturing
0.2032
0.2657
0.1117
Union- Pk(IND)
(3.78)
(4.78)
(1.69)
0.0579
0.1662
0.3183
Union- Pm(SMSA)
(1.32)
(0.32)
(0.94)
0.3574
0.1677
0.3112
Nonunion - Pk(IND)
(3.23)
(2.96)
(1.56)
-0.0997
-0.3133
-0.0603
Nonunion - Pm(SMSA)
(-0.19)
(-0.35)
(-1.04)
Production workers: nonmanufacturing
0.3523
0.4338
0.3587
Union- Pk(IND)
(7.15)
(8.44)
(6.35)
1976
1977
1978
1979
0.2419
(4.42)
0.4578
(2.49)
0.2569
(2.35)
0.1989
(0.65)
0.3204
(5.88)
0.5785
(3.46)
0.1870
(2.12)
0.3681
(1.55)
0.3908
(5.92)
0.2240
(1.10)
0.2519
(2.57)
0.0310
(0.10)
0.2500
0.3966
(3.31)
(3.45)
0.2957
0.1098
(1.33)
(0.32)
0.4056
0.0817
(3.20)
(0.49)
0.0580 -0.3739
(0.17) (-0.79)
0.4482
(7.69)
0.3863
(7.35)
0.4732
(8.34)
0.3292
(4.18)
1980
0.3249
(3.72)
Union - Pm(SMSA)
Nonunion-
Pk(IND)
Nonunion - Po(SMSA)
Nonproduction workers
Union - Pk(IND)
UnionPo-
(SMSA)
Nonunion - Pk(IND)
Nonunion - Po(SMSA)
0.1435 -0.3503
-0.1115
0.0813
-0.2130
-0.1911
0.1450
0.2550
(-1.27)
(0.46)
(0.68) (-2.04)
(-0.53)
(-0.99)
(0.53)
(0.80)
0.7152
0.6651
0.5924
0.5668
0.5845
0.6192
0.5366
0.4234
(7.63)
(7.14)
(6.44)
(7.10)
(7.49)
(4.50)
(7.24)
(3.57)
-0.0205
0.4298
0.0559 -0.2334
-0.1323
-0.0680
-0.5160
-0.0737
(-2.31)
(-0.09)
(-0.64)
(2.03)
(0.31) (-1.05)
(-0.23)
(-0.23)
0.0873
(1.22)
-0.2493
(-0.97)
0.3907
(7.72)
0.0895
(0.55)
Note: t-statistics in parentheses.
0.1270
0.1876
(1.48)
(2.17)
0.0196 -0.0787
(0.06) (-0.26)
0.3104
0.3466
(6.36)
(6.84)
0.1793
0.1532
(1.09)
(0.94)
0.2259
(2.35)
0.0142
(0.04)
0.3256
(6.27)
0.3419
(2.10)
0.2089
0.0954
0.2304
0.0011
(2.50)
(1.21)
(2.38)
(0.01)
0.1470 -0.3340
-0.6410
0.0283
(-1.86)
(0.54) (-1.18)
(0.05)
0.2383
0.3126
0.1812
0.3287
(5.01)
(6.28)
(2.90)
(4.24)
0.2701
0.1221
0.1029 -0.3458
(1.86)
(0.74)
(0.50) (-1.33)
146
The Journal of Human Resources
become widespread, a brief discussion of results seems warranted (we are
unaware of other studies including both industry and SMSA density). Table
2 presents the coefficients y and 6 on the density variables Pk and P,
respectively, from the union and nonunion wage equations.
Industry union density, Pk, is found to positively and significantly affect
both union and nonunion wages (for comparison with other studies, see
Freeman and Medoff 1981, Antos 1983, Moore, Newman, and Cunningham
1985, and the survey by Lewis 1986). The positive effect of increased density
on union wages is typically interpreted as resulting from a decreased labor
demand elasticity. The positive effect of density on nonunion wages is
thought to result primarily from a dominant threat effect in which nonunion
employers must increase wages as industry density increases in order to
remain nonunion. Or alternatively, nonunion firms can pay higher wages
and be at less of a competitive disadvantage the greater is industry-wide
coverage (see Freeman and Medoff 1981 and Moore, Newman, and Cunningham 1985 for related discussions).
In contrast to industry density, labor market (SMSA) union density has
little clear-cut impact on union or nonunion wages (see Holzer 1982 for
more detailed evidence on SMSA density). The greater significance of Pk
than Pm on union wages is consistent with the argument that industry
coverage, but not labor market coverage, impacts on the elasticity of labor
demand. The minor net impact of Pm on nonunion wages suggests that
threat effects from SMSA density, to the extent they exist, are offset by
spillover (or surplus labor) effects that place downward pressure on nonunion wages. While labor spillover effects are likely to be captured by measures of SMSA density (assuming imperfect interarea mobility), they seem
less likely to be associated with industry density.
Comparison of the density coefficients from the union and nonunion
equations in Table 2 also permit inferences as to their effect on the size of the
wage differential. The finding that yu > yn implies the union wage gap
increases with industry density, while 6u > an implies the gap increases with
SMSA density. Surprisingly we do not find the wage gap increasing with
industry density, as theory and limited past evidence would predict (Freeman and Medoff 1981). However, we are reluctant to draw strong inferences
based on the relative magnitudes of the density coefficients, since it seems
likely they are proxying for other omitted variables (Lewis 1986, 153).7
Coefficient estimates on SMSA density do suggest, however, that labor
market density has no significant impact on the magnitude of the union wage
gap.
7. Indeed, Moore, Newman, and Cunningham (1985) find that the nonunion industry density
coefficient is sharply reduced for a sample of manufacturing workers when a firm size variable is
included.
Communications
V. Summary
This paper has provided a detailed analysis of nominal and
real union-nonunion relative wage effects during the 1973-83 period. For all
years, differences between the nominal and real union wage effects are
small. No difference is found for production workers in manufacturing,
while approximately a one percentage point difference is found for production workers outside of manufacturing. Based on these results, it is concluded that for most research endeavors in this area, the costs of considering
cost-of-living differences (e.g., restricting the sample) outweigh the benefits.
Evidence has also been provided on the union wage gap over the 1973-83
period and the effects of both industry and SMSA density on union and
nonunion wages. Union-nonunion wage differentials appear to have widened during the 1976-78 period, but returned to earlier levels after 1978.
Industry density was found to increase significantly both union and nonunion wages, whereas labor market density appears to have little significant
impact on union or nonunion wages.
Barry T. Hirsch
North
Carolina
at Greensboro
University of
John L. Neufeld
University of North Carolina at Greensboro
References
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Freeman,RichardB. 1981. "The Effect of Unionismon Fringe Benefits."
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. 1984. WhatDo UnionsDo? New York: Basic Books, 1984.
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Kennedy, Peter E. 1981. "Estimation with Correctly Interpreted Dummy
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