View
220
Download
0
Category
Preview:
Citation preview
Does measurement error bias ®xed-effectsestimates of the union wage effect?�
Joanna K. Swaffield
Centre for Economic Performance, London School of Economics.
I. Introduction
The estimation of the union wage differential has become increasingly
re®ned as improved data have become available. Just as micro-level data
heralded the start of improved estimates over those using aggregate data the
availability of individual-level panel data offered a further improvement.
However, whereas estimates of the union wage effect were undoubtedly
improved by the use of cross-section individual-level rather than aggregate
data, the equivalent advantage of panel over cross-section estimates is far less
clear.
If the observed union wage differential is a result of systematic product-
ivity differences between union and non-union workers and some or all of
these productivity differences are not observed in the data, cross-section
estimates of the union wage differential will be biased. This bias can
potentially be removed through the estimation of the union wage differential
with panel data or by simultaneous equation methods, which control for
unobserved heterogeneity. Unfortunately, simultaneous equation methods
require an instrument that is correlated with union status but not with the
wage. The generation of persuasive estimates of the union wage differential
under these models requires the instruments to be convincing. The alternative
method of controlling for unobserved heterogeneity, by using panel data,
does not require instruments. However, this does not mean that the panel
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 63, 4 (2001) 0305-9049
# Blackwell Publishers Ltd, 2001. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350
Main Street, Malden, MA 02148, USA.
437
�I thank Steve Nickell, Mark Stewart, an anonymous referee and seminar participants at theCentre for Economic Performance, London School of Economics and the Manchester LabourEconomics seminar, Department of Economics, University of Manchester for helpful comments,and the ESRC Corporate Performance Programme of the Centre for Economic Performance for®nancial support. The BHPS data used in this paper were collected by the ESRC Research Centreon Micro-social Change at the University of Essex and made available through the ESRC DataArchive. Neither bears any responsibility for the analyses or interpretations presented here.
estimates of the union wage effect are automatically superior to cross-section
estimates.
Comparisons of cross-section and panel estimates of the union wage effect
have been well documented in the US literature (see Mellow (1981), Mincer
(1983), Freeman (1984), Jakubson (1991) and Card (1996)), tending to
conclude that cross-section estimates are upwardly biased (Lewis (1986)).
However, the evidence also suggests that ®xed-effects estimates tend to be
biased downwards. For instance, Freeman (1984), using data from the CPS,
NLS, PSID and QES, shows ®xed-effects estimation to suffer from poten-
tially severe measurement error that biases downwards panel estimates. Card
(1996), using an estimation method that explicitly accounts for misclassi®ca-
tion error in reported union status, ®nds that `for the sample as a whole the
[measurement-error] corrected [longitudinal] estimator is almost identical to
the cross-sectional wage gap (17% versus 15±16%)' (pp. 974). Mincer
(1983), using PSID and NLS data, ®nds panel estimates to be smaller than
cross-section union estimates but highlights the problem of union changes
without job changes. This leads Mincer (1983) to conclude that `the ®gures
for job stayers who change union status appear to be in¯ated by misreporting
or misclassi®cation' (pp. 222).
Whether the general conclusions in the US literature are fundamentally
different for the British labour market is an empirical question. Relatively
little research has yet been undertaken to investigate this owing to the lack of
data. However, in recent work Andrews et al. (1998a), using the New
Earnings Survey Panel Data set (NESPD) 1978 and 1985, ®nd that cross-
section estimates of the wage effect of coverage are approximately 4 percent
and ®xed-effects panel estimates are 2 percent.1 Hildreth (1999), using data
from the BHPS waves 1 and 5 for private sector male and female employees,
concludes that `male workers are union members from positive selection in
the production sector, but negatively selected in the service sector' (pp .15).
For women, union membership appears to result from negative selection,
where in both cases union membership is conditional upon union coverage.
Blanch¯ower (1997), using the BHPS waves 1, 2 and 3, presents evidence
that cross-section estimates of union membership are upwardly biased.
Using data from the British Household Panel Survey (BHPS) waves 1 to 6
(1991±1997), this paper investigates whether the general conclusions from
the US literature, on comparisons of cross-section and ®xed-effects estimates
of the union wage effect and the impact of measurement error, hold for
British data.
1Coverage is de®ned as the employee being covered by a negotiated collective agreement, whichaffects pay and/or conditions of employment. In the BHPS coverage is de®ned as if `there is a tradeunion or similar body such as a staff association recognized by your management for the negotiatingpay or conditions for the people doing your sort of job in your workplace '.
438 Bulletin
# Blackwell Publishers 2001
II. Data, Sample and Variables De®nitions
The two regression samples used throughout the paper are unbalanced panel
samples of female employees and male manual full-time employees.2 Results
for both the female employee and male manual full-time employee samples
are presented for two main reasons. Firstly, although the most often used
sample for union wage effect estimation is male manual workers, unions raise
the relative wages of lower paid workers of whom women make up a larger
proportion than men. Secondly, choosing these two samples provides a
comparison between one (the male manual full-time employee sample) which
could be argued to suffer from sample selection bias and the other (the full
female employee sample) possibly open to criticism on the basis of false
homogeneity assumptions.3 Each sample includes employees (not full-time
students) who were original sample members aged 18±65 with no missing or
imputed data.4 The wage equation is a function of human capital variables
including age at which the person last left full-time education, potential
labour market experience, tenure length with the employer, along with
controls for type of ®rm in which employed (such as ®rm size and oc-
cupation).5 The wage measure is (log) gross average (nominal) hourly
earnings, with wave dummies included for each wave other than the base
group.6
Male manual employees are the `traditional' sample for estimating the
union wage effect. Historically unions have had a greater power base and
been more active within the (lower paid) manual rather than non-manual
occupations. This distinction is particularly so for men as the manual and
non-manual occupations are strongly indicative of type of employment in
terms of skill, educational attainment and remuneration etc. At ®rst sight the
argument for restricting the sample to full-time workers may appear less
compelling as the dependent variable is de®ned as the hourly wage and a
part-time control could have been included in the wage equation (as in the
female regression). However, including the part-time employees would have
2The unbalanced panel sample has a minimum of two wage observations per individual. With®xed-effects estimators the minimum number of observations per individual has to be two,otherwise the individual would just drop out of the model. The unbalanced rather than balancedpanel sample was chosen for analysis due to the information loss and potential sample selection biasthat is present within balanced panel samples.
3Although the female sample will not suffer from the potential sample selection bias caused byrestricting the employee group to only manuals, there still remains the possibility that the femalesample suffers from sample selection bias caused by the participation decision.
4Only original sample members were included, as these were the individuals, in the households,that were randomly selected at the start of the BHPS.
5See Appendix A, Table A.1 for a full list of variables and sample means.6Using hourly rather than weekly earnings may slightly raise the union wage differential as union
workers tend to work fewer hours per week on average than non-union workers (Oswald & Walker(1993), Stewart & Swaf®eld (1997)).
Does measurement error bias ®xed-effects estimates of the union wage effect? 439
# Blackwell Publishers 2001
yielded relatively small gains in sample size at the expense of a potential
increase in the heterogeneity of the sample.
By contrast, the female sample includes full-time, part-time, manual and
non-manual employees. Firstly, the full-time/part-time distinction was ignored
on the grounds that (unlike for men) the exclusion of part-time female employ-
ees would have been likely to cause a serious sample selection bias in the
panel, since women are more likely to move between these states over a
working lifetime and within this six period panel. Secondly, both manuals and
non-manuals were included in the sample as the distinction between the two
groups was considered to be far less marked (in terms of skill, wage etc) than
for male employees. Non-manual women tend to be at the lower skill end of
the non-manual group, and so their earnings are similar to those of manual
workers. As a result the distinction between the union wage effects for manual
and non-manual workers is not as apparent for females as it is for males.7
In each wave of the BHPS employees are surveyed concerning their union
status. In waves 1, 5 and 6 the employment section union questions were put
to all employees. Unfortunately in waves 2, 3 and 4 this was not the case:
only those employees who changed job/position since 1st September of the
previous year and/or were not surveyed in the previous wave were asked all
the union status questions as part of the employment questionnaire. This
produced a serious discontinuity in the BHPS survey data, with implications
for panel use of the union status data. However, in each of waves 1 to 5 an
additional union membership question was asked, as part of the `values and
opinions'section of the BHPS questionnaire.
The questions in the employment section of the BHPS permit the con-
struction of union variables for union coverage (cover) and union member-
ship (member). The second membership question (in the BHPS values and
opinions section) permits a second separate variable to be constructed to
measure union membership (member V). For all six BHPS waves, the best
measure of union status available is union membership (taken from the values
and opinions section of the BHPS questionnaire).8
7For example, the raw union membership wage differential (calculated as a percentage of thenon-union wage) for the female employee pooled cross-section sample is similar across the sixoccupational groups. The raw union membership wage differential is approximately 24.4% forprofessionals, 36.7% for intermediate non-manuals, 36.0% for foreman and skilled manuals, 26.3%for semi-skilled manuals, 11.2% for unskilled manuals and 6.8% for agricultural workers. Overallthe raw female manual union membership wage differential is 28.5% compared to the raw non-manual union membership wage differential of 36.5%. By contrast, for men we have a raw unionmembership wage differential of 22.8% for manual workers and 10.4% for non-manual.
8Its worth noting that all wave 6 `member V' values are replaced by the union membership(member) value from the employment section. This is because the values and opinions section didnot include the second trade union membership question at wave 6. Although this will produce adegree of discontinuity, due to the question de®nitions, this was felt to be outweighed by the samplesize improvements and having a full panel of the ®rst six BHPS waves.
440 Bulletin
# Blackwell Publishers 2001
For waves 1, 5 and 6 information is available on both the employee's
union status in terms of membership of the union and whether the union
covers them for the purpose of collective bargaining. Therefore, three
additional union status groups can be de®ned, these are `covered member'
(tmcv), `covered non-member' (ntmcv) and the base group of `uncovered'
(regardless of membership status). These are important union variables to
consider as analysis of the union wage differential at the establishment points
towards those with a closed shop or high union density having an above-
average differential. At the individual-level, whilst members and non-mem-
bers doing the same job in the same establishment will earn the same, when
comparing across establishments membership will be a closer indicator of
the differential than coverage. In short, the conditional probability of a closed
shop or high union density is greater given membership than given cover-
age.9
III. Estimates of the Union Wage Effect
In estimating the union wage effect the ®rst question to address is: which
union wage effect to estimate ± the impact of union coverage, union
membership or membership conditional upon coverage? The second question
is: which estimator to use ± cross-section OLS, between-effects, random-
effects or ®xed-effects?
Some general points concerning the choice between these estimators
should ®rst be made. For example, is the ®xed-effects or random-effects the
superior panel estimator? The fundamental difference between the estimators
is that the random-effects estimator assumes that there is no correlation
between the explanatory variables and the unobservables. If part of the union
wage differential is due to higher productivity workers having union status,
the unobservable will be correlated with the union status variable. If this
is the case the assumption of the random-effects estimator will be violated
and the estimates will not be consistent and ef®cient.
A second general point relates to comparisons between pooled OLS and
panel estimates. If the errors in the pooled OLS equation are correlated
across individuals across time the residuals will not ful®l the classical linear
regression (CLR) assumption of being identical and independently distribu-
ted (i.i.d). This problem could be dealt with in a number of ways. One is to
separate the waves of data in the pooled sample into separate equations such
that for each individual there is only one wage observation in each equation.
9The basic problem is that coverage multiplied by density is a potentially important omittedvariable. If density at the establishment was observed then this effect could be convincinglycontrolled for. See Andrews et al (1998b) for discussion of this point.
Does measurement error bias ®xed-effects estimates of the union wage effect? 441
# Blackwell Publishers 2001
Alternatively, the equation could be estimated using the between-effects
estimator, where an average of each variable in the equation is taken for each
individual across all the time periods.10 A third approach is to estimate the
original OLS equation under a Generalized Least Squares (GLS) equation.11
If the standard errors in the classical linear regression are not i.i.d then the
off diagonals of the variance-covariance matrix will not equal zero. The GLS
equation minimizes a weighted sum of squared residuals rather than the sum
of squared residuals as in the CLR.
In Table 1 estimates of the union wage effect for the female (manual and
non-manual, full-time and part-time) and male manual full-time employee
10All between-effects estimates based on the unbalanced panel sample use weighted least squares(WLS) rather than OLS. Both methods produce consistent estimates. The estimates are notsubstantially affected by this choice. It is worth noting though that the between-effects estimatorrequires the same assumption of no correlation between the explanatory variables and the residuals,as does the random-effects (GLS) estimator. In fact, if this assumption does hold, the random-effects(GLS) estimator is more ef®cient than the between-effects estimator as the between-effectsestimator discards information over time in favour of simple sample means.
11The GLS estimates can be considered as both panel and cross-section estimates. All thatdistinguishes GLS from the OLS estimates is that the OLS restriction that the residual does notcontain a person effect, íi, is not applied in the GLS. In the GLS equation the random distributionapplied to the standard residual or error is also applied to the person-speci®c effect íi. To clarifyfurther, the variance minimising weight (j) in the GLS equation is a function of the variance ofperson-speci®c effect íi and the residual ui. If the variance of the person-speci®c effect íi isassumed to equal zero (so íi is always equal to zero) j will also equal zero, and therefore the GLSequation is exactly equivalent to the OLS equation.
TABLE 1
Estimates of the Union Wage Effect
OLS Between-effects
Random-effects
(GLS) Fixed-effects
(1) (2) (3) (4)
Waves 1-6
Female employees
Member V 0.098 (9.19) 0.098 (4.28) 0.079 (7.92) 0.052 (4.82)
Adj. R2 0.461 0.561 0.430 0.178
Hausman (1978) test ± ± ÷2(30) � 658:66a ±
Sample 8,673 8,673 8,673 8,673
Male manual full-time employees
Member V 0.116 (8.34) 0.117 (4.39) 0.092 (6.22) 0.064 (3.64)
Adj. R2 0.317 0.403 0.303 0.199
Hausman (1978) test ± ± ÷2(27) � 140:91a ±
Sample 3,187 3,187 3,187 3,187
442 Bulletin
# Blackwell Publishers 2001
TABLE 1
(continued)
OLS Between-effects
Random-effects
(GLS) Fixed-effects
(1) (2) (3) (4)
Waves 1, 5 & 6
Female employees
Tmcv 0.129 (6.58) 0.118 (3.82) 0.144 (7.18) 0.132 (5.07)
Ntmcv 0.032 (1.57) 0.027 (0.80) 0.044 (2.27) 0.057 (2.45)
Adj. R2 0.484 0.555 0.475 0.287
Hausman (1978) test ± ± ÷2(28) � 235:08a ±
Cover 0.085 (4.83) 0.081 (2.87) 0.091 (5.26) 0.086 (4.03)
Adj. R2 0.480 0.552 0.471 0.284
Hausman (1978) test ± ± ÷2(27) � 232:22a ±
Member 0.110 (6.77) 0.099 (3.92) 0.121 (7.13) 0.103 (4.61)
Adj. R2 0.483 0.555 0.475 0.286
Hausman (1978) test ± ± ÷2(27) � 242:93a ±
Member V 0.110 (6.69) 0.105 (3.88) 0.108 (6.89) 0.082 (4.38)
Adj. R2 0.483 0.554 0.475 0.285
Hausman (1978) test ± ± ÷2(27) � 233:02a ±
Sample 3,457 3,457 3,457 3,457
Male manual full-time employees
Tmcv 0.080 (3.35) 0.073 (2.08) 0.077 (2.95) 0.049 (1.19)
Ntmcv 0.055 (1.90) 0.022 (0.47) 0.075 (2.62) 0.089 (2.51)
Adj. R2 0.317 0.377 0.321 0.313
Hausman (1978) test ± ± ÷2(25) � 53:91a ±
Cover 0.071 (3.37) 0.059 (1.82) 0.076 (3.44) 0.073 (2.37)
Adj. R2 0.317 0.376 0.321 0.313
Hausman (1978) test ± ± ÷2(24) � 52:88a ±
Member 0.077 (3.45) 0.077 (2.31) 0.070 (2.94) 0.044 (1.23)
Adj. R2 0.317 0.378 0.321 0.309
Hausman (1978) test ± ± ÷2(24) � 314:13a ±
Member V 0.082 (3.70) 0.075 (2.22) 0.081 (3.49) 0.071 (2.09)
Adj. R2 0.318 0.378 0.323 0.312
Hausman (1978) test ± ± ÷2(24) � 314:13a ±
Sample 1,220 1,220 1,220 1,220
Notes:aNull hypothesis of the Hausman (1978) test rejected at 1%.bAdjusted R-squared in the table refers to overall R-squared for random-effects (GLS), between
R-squared for between-effects and within R-squared for ®xed-effects estimates.cSample sizes refer to unbalanced panel samples and asymptotic t-ratios are in parentheses.
Does measurement error bias ®xed-effects estimates of the union wage effect? 443
# Blackwell Publishers 2001
samples are shown. In column 1 the OLS estimates of the various union wage
effects are shown. These results con®rm (as do the equivalent between-effects
estimates) the standard result in the British literature, that the return to union
membership is greater than the return to union coverage and the return to
union membership conditional upon coverage (tmcv) is greater than coverage
alone (ntmcv). For example, covered member (tmcv) and covered non-
member (ntmcv) wage effect estimates are 0.129 (t-ratio 6.58) and 0.032
(t-ratio 1.57) respectively for the female sample. While the equivalent sample
wage effect estimates for union coverage and union membership are 0.085
and 0.110 respectively (both signi®cant).
For females the union membership (member V) wage effects are 0.079
estimated under the random-effects (GLS) estimator and 0.052 under the
®xed-effects estimator (both signi®cant). For males the equivalent estimates
are 0.092 (random-effects) and 0.064 (®xed-effects), again both signi®cant.
A comparison of panel estimates of union membership wage effects with the
cross-section OLS estimates appears to provide evidence that the OLS
estimates are upwardly biased, suggesting that unobserved heterogeneity is
positively correlated with union status.12
The ®xed-effects and random-effects (GLS) estimates of the covered
member (tmcv) wage effect con®rm the above ®ndings for males. Random-
effects (GLS) and ®xed-effects estimates of the union wage effect fall from
the OLS estimates of 0.080 to 0.077 and 0.049 respectively. In contrast, the
estimates of the covered non-member (ntmcv) wage effect rises under both
panel estimators. For women, both the covered member and covered non-
member wage effect estimates rise. These results suggest that OLS estimates
are downwardly biased, implying that the unobserved heterogeneity is
negatively correlated with union status.13 Estimates of union coverage under
cross-section and panel estimators show little change for either sample. For
union membership, ®xed-effects estimates are below the OLS estimates for
both samples.
The GLS estimates are generally similar in magnitude and signi®cance to
those of the pooled OLS equation. The ®xed-effects estimates are smaller in
signi®cance and magnitude than the GLS (random-effects) estimates. Esti-
mates for union member and covered union member suggest that unobserved
heterogeneity is positively correlated with union status, leading to an upward
bias in the cross-section estimates. The null hypothesis of the Hausman
12These results are similar to those presented in Blanch¯ower (1997). BHPS union membershipcross-section estimates across waves 1-3 are reported to fall from 0.1457 to 0.0359 for women under®xed-effects estimators and from 0.0618 to 0.0317 for men.
13The magnitude of these estimates for covered member are similar to those presented in Hildreth(1999) where the impact of membership conditional on coverage estimated under a ®xed-effectsestimator is reported as 0.1243 for female workers.
444 Bulletin
# Blackwell Publishers 2001
(1978) test, that (assuming correct model speci®cation) there is no correlation
between explanatory variables and unobservables, is rejected for all random-
effects (GLS) estimates in Table 1. Therefore, more weight should be placed
upon the union wage effect estimated under the ®xed-effects rather than
random-effects estimator.
To summarize, if OLS estimates suffer from omitted variable bias (in
particular unobserved heterogeneity bias) the estimates of the union wage
effect will not be convincing. Estimating the wage equation with panel data
should remove this potential bias, and comparisons with the cross-section
estimates should provide evidence for the direction and magnitude of bias.
Comparisons of the OLS and ®xed-effects estimates above would seem to
suggest that OLS union wage effect estimates are upwardly biased. However,
this conclusion relies on the ®xed-effects estimator producing unbiased
estimates that are `superior' to those based on OLS. The remainder of the
paper investigates whether this is likely to be the case by focussing on the
impact of measurement error on ®xed-effects estimates.14
IV. Measurement Error Bias in the Fixed-effects Estimates of theUnion Wage Effect
Measurement error will cause OLS and ®xed-effects estimates to be biased
towards zero and inconsistent.15 However, the measurement error bias is
likely to be more exaggerated in the ®xed-effects estimates, for two reasons:
random misclassi®cation in two periods will produce a larger number of
misclassi®ed workers than in one period and, due to the small number of
union changes that identify the ®xed-effects estimate of the union wage
effect, the proportion of observations in error will be greater (Freeman
(1984)).16
In the remainder of the paper three main methods are used to reduce the
(likely) measurement error in the union status variable: ®rstly by comparing
responses from the two membership questions asked in the survey, secondly,
by re-constructing the union variable over time so that changes in union
status (observed after the initial period) only occur when the individual
14A number of issues are also important here such as sample selection bias and identi®cation (seeSwaf®eld (1998) for a discussion of these points).
15The union status variable and the measurement error are negatively correlated. This correlationarises because when the union status variable equals 1 the measurement error will be 0 or ÿ1 andwhen the union status variable equals 0 the measurement error will be 0 or 1.
16The measurement error bias is exaggerated in the ®xed-effects estimates, as the variance of thetrue union status variable is less than the variance of the measurement error in the union changes.This is due to serial correlation in the union status variable across time and weak or no serialcorrelation in the measurement error.
Does measurement error bias ®xed-effects estimates of the union wage effect? 445
# Blackwell Publishers 2001
changes employer (and/or job), thirdly, by using averages to reduce the
measurement error in the union status variables.17
Measurement error in the union membership response
Waves 1 and 5 of the BHPS questionnaire contain two questions on union
membership asked unconditionally of all respondents. These two membership
questions allow a check both of whether the individual is reporting consis-
tently and whether we are measuring what we think we are. If the individual
answered `yes' to the values and opinions section question on union member-
ship (i.e. are you a member of a trade union) he or she should also have
answered `yes' to whether they belong to a trade union or a similar body
recognised by management for bargaining. This is because the values and
opinions trade union membership question is a narrower de®nition of
membership, i.e. it applies only to trade unions and not to staff associations.
Observations with answers (yes, no) to these questions are categorised as
measurement error (meA 6� 0). Answers (no, yes) suggest that the individual
belongs to a staff association but not a trade union, and are labelled as
meB 6� 0.
In Table 2, the impact of restricting the samples on the basis of the
measurement error (meB) assessments are shown for waves 1 and 5.18 For
both female and male samples, the restriction of union membership to trade
unions rather than trade unions and other staff associations increases the
union impact on the wage under each of the union de®nitions and under both
the OLS and ®xed-effects estimators. These results suggest that the inclusion
of worker organizations which are not formally de®ned by the employee as
trade unions result in a downward bias on the effect of the `trade union' on
the wage.
17The measurement error in the union status variables can arise from three sources. Firstly,individuals may misreport their true union status, secondly the interviewer may record the wrongresponse, and ®nally there may be errors in entering the response recorded by the interviewer intothe data. In the case of the last two sources one can clearly see how misclassi®cation of the trueresponse can arise. In the case of the individual's own response it could be the case that a worker iscovered by a union for the purposes of pay bargaining and is not aware of it, and likewise they mayassume they are when they are not. Such incorrect reporting by the individual seems clearlypossible. Individual errors in reporting union membership status are slightly less clear. If anindividual is not a member, why would they think that they are? They could be a lapsed unionmember or they may think membership of some professional body is equivalent to that of a tradeunion when it is not. How the opposite reporting error arises is less clear. However, the importantpoint is that very few misclassi®cations are required for the measurement error to affect the ®xed-effects estimates as relatively few union changes drive the ®xed-effects estimates of the union wageeffect.
18As wave 6 of the BHPS does not contain the trade union membership question in the value andopinions section and waves 2, 3 and 4 do not contain unconditionally asked union questions in theemployment sections.
446 Bulletin
# Blackwell Publishers 2001
Comparisons of similar questions concerning union membership highlight
very few inconsistent responses.19 Either there is very little measurement
error or individuals respond consistently (although not necessarily correctly)
when asked the same or very similar questions over a short period of time.
Although this method of investigating measurement error was not very
TABLE 2
Union Wage Effect Estimates with Measurement Error Sample Restrictions
Full sample meB � 0
OLS Fixed-effects OLS Fixed-effects
Waves 1 & 5
Female employees
Tmcv 0.121 (4.56) 0.137 (3.55) 0.151 (4.78) 0.165 (3.64)
Ntmcv 0.054 (1.93) 0.090 (2.64) 0.057 (1.87) 0.098 (2.67)
Adj. R2 0.489 0.354 0.486 0.351
Cover 0.092 (3.83) 0.108 (3.45) 0.101 (3.67) 0.118 (3.43)
Adj. R2 0.488 0.352 0.483 0.349
Member 0.091 (4.13) 0.082 (2.45) 0.113 (4.35) 0.095 (2.39)
Adj. R2 0.489 0.348 0.485 0.344
Sample 1,820 1,820 1,568 1,568
Male manual full-time employees
Tmcv 0.129 (4.09) 0.089 (1.56) 0.143 (4.34) 0.117 (1.97)
Ntmcv 0.080 (1.98) 0.075 (1.45) 0.082 (2.02) 0.079 (1.53)
Adj. R2 0.316 0.359 0.319 0.362
Cover 0.113 (4.00) 0.081 (1.85) 0.122 (4.19) 0.095 (2.11)
Adj. R2 0.315 0.359 0.318 0.361
Member 0.097 (3.25) 0.055 (1.14) 0.115 (3.69) 0.074 (1.49)
Adj. R2 0.309 0.355 0.313 0.356
Sample 628 628 596 596
Notes:aAdjusted R-squared in the table refers to within R-squared for ®xed-effects estimates.bSample sizes refer to unbalanced panel samples and asymptotic t-ratios are in parentheses.cmeB equals zero if the two membership question responses exclude membership of staff
associations.
19Restrictions to the sample based on meA are not presented here, as very few individuals appearto have this form of identi®ed measurement error. For the male manual full-time employee samplenone of the responses to the two membership questions are inconsistent. For the female sample onlyfour observations show this inconsistency in either wave 1 and/or 5 and estimates are the same if notextremely similar for the restricted sample (meA � 0).
Does measurement error bias ®xed-effects estimates of the union wage effect? 447
# Blackwell Publishers 2001
enlightening, it did show that returns to formal trade union status appear
slightly larger than those to any employee representation.
Restricting union changes to those with employer and/or job changes
A second method to identify measurement error bias in the union estimates is
to restrict changes in the union status variable to only those that have a higher
probability of being a true change ± those who change employers and/or jobs
over the same period.20
In Table 3, the union wage effect for each of the three union de®nitions is
shown for union changes restricted to those who also experience a change in
employer and/or job change across the waves 1, 5 and 6 and waves 1 to 6
samples. For the female employee sample comparisons with Table 1 (the
original estimates) suggests that the ®xed-effects estimates for covered
member, coverage and membership (member and member V) are down-
wardly biased. For the male manual full-time sample, the ®xed-effects
estimated returns to union membership (member V) and coverage increase
quite considerably when the changes in union status are restricted.21
Waves 2, 3 and 4 of the BHPS do not contain unconditionally asked
questions in the employment section for trade union coverage and member-
ship. However, if the union status is de®ned as that of the ®rst observed
period, with changes to this status only if an accompanying employer (and/or
job) change occurred, (as in Table 3), the data in these three waves can be
used. In Table 4 the estimated union wage effect, under the three de®nitions
of union, are shown for all six waves. Although these results cannot be
compared with the unrestricted or `original' union estimates, they do provide
an interesting comparison with the ®gures in Table 3. Table 4, with a larger
sample size than Table 3 shows the female estimates to be smaller. In
comparison, the male manual full-time estimates (under both ®xed-effects
and OLS) appear downwardly biased in Table 3 (particularly in the case of
union membership).
De®ning union changes to occur only when employer or job changes
occur, a comparison of the measurement error described in the previous
20The distinction between job and employer changes is that an individual who changes job doesnot have to change employer. Therefore all employer changes are job changes but not all jobchanges are employer changes.
21An alternative method to including this adjusted union status variable in the wage equationwould be to use an instrumental variable i.e. one correlated with the true union status variable butnot the measurement error. Additional estimates (not presented here) were found that used thisadjusted union status variable (i.e. union changes restricted to changes with employer and/or jobchange) as an instrument rather than as an alternative regressor. The results also provided evidencethat (conditional upon the assumption of no correlation between measurement error and theinstrument) measurement error biases downwards the ®xed-effects estimates of the union wageeffect.
448 Bulletin
# Blackwell Publishers 2001
section by deviation between the `member' and `member V' responses can
also be made for waves 1 to 5. In Table 4, the restricted sample estimates for
consistent union membership responses (meA � 0) and the stricter de®nition
of union membership (meB � 0) are shown for the full female and male
TABLE 3
Union Wage Effect Estimates with Union Status Changes Restricted to Employer or Job
Changers
Female Male manual full-time
OLS Fixed-effects OLS Fixed-effects
Waves 1, 5 & 6
Union Ä if Employer ÄTmcv 0.141 (7.12) 0.167 (4.75) 0.073 (3.06) 0.034 (0.63)
Ntmcv 0.038 (1.90) 0.046 (1.43) 0.060 (2.15) 0.170 (2.98)
Adj. R2 0.485 0.286 0.316 0.316
Cover 0.090 (5.12) 0.097 (3.48) 0.068 (3.26) 0.097 (2.27)
Adj. R2 0.480 0.283 0.316 0.312
Member 0.118 (7.17) 0.143 (4.45) 0.055 (2.48) 0.018 (0.35)
Adj. R2 0.484 0.285 0.314 0.307
Union Ä if Job ÄTmcv 0.139 (6.97) 0.171 (5.34) 0.071 (3.01) 0.031 (0.60)
Ntmcv 0.037 (1.84) 0.067 (2.36) 0.062 (2.20) 0.173 (3.18)
Adj. R2 0.484 0.288 0.316 0.317
Cover 0.089 (5.03) 0.109 (4.20) 0.068 (3.26) 0.097 (2.27)
Adj. R2 0.480 0.285 0.316 0.312
Member 0.116 (7.00) 0.136 (4.88) 0.053 (2.40) ÿ0.003 (0.06)
Adj. R2 0.484 0.287 0.314 0.307
Sample 3,457 3,457 1,220 1,220
Waves 1±6
Union Ä if Employer ÄMember V 0.098 (9.08) 0.063 (3.14) 0.089 (6.47) 0.126 (4.34)
Adj. R2 0.461 0.177 0.311 0.201
Union Ä if Job ÄMember V 0.104 (9.67) 0.077 (4.48) 0.093 (6.78) 0.094 (3.55)
Adj. R2 0.462 0.178 0.312 0.199
Sample 8,673 8,673 3,187 3,187
Notes:aAdjusted R-squared in the table refers to within R-squared for ®xed-effects estimates.bSample sizes refer to unbalanced panel samples and asymptotic t-ratios are in parentheses.
Does measurement error bias ®xed-effects estimates of the union wage effect? 449
# Blackwell Publishers 2001
TABLE 4
Union Wage Effect Estimates with Union Status Changes and Measurement Error Sample Restrictions
Waves 1±6 Waves 1±5 Waves 1±5 Waves 1±5
Full Full meA � 0 meB � 0
OLS Fixed-effects OLS Fixed-effects OLS Fixed-effects OLS Fixed-effects
(1) (2) (3) (4) (5) (6) (7) (8)
Female employees
Tmcv 0.124 (9.40) 0.112 (5.08) 0.123 (8.61) 0.122 (4.79) 0.122 (8.55) 0.121 (4.76) 0.137 (8.71) 0.135 (4.59)
Ntmcv 0.040 (3.04) 0.085 (4.28) 0.042 (2.93) 0.105 (4.36) 0.041 (2.90) 0.105 (4.34) 0.044 (3.03) 0.113 (4.40)
Adj. R2 0.471 0.190 0.472 0.174 0.472 0.174 0.466 0.171
Cover 0.081 (7.02) 0.097 (5.56) 0.082 (6.55) 0.113 (5.49) 0.081 (6.49) 0.113 (5.46) 0.084 (6.32) 0.122 (5.43)
Adj. R2 0.468 0.190 0.469 0.174 0.469 0.174 0.463 0.171
Member 0.106 (9.56) 0.080 (3.87) 0.105 (8.74) 0.076 (3.19) 0.104 (8.70) 0.075 (3.15) 0.115 (8.74) 0.071 (2.56)
Adj. R2 0.471 0.188 0.472 0.171 0.472 0.171 0.466 0.167
Sample 7,838 7,838 6,598 6,598 6,591 6,591 6,092 6,092
450
Bulletin
#B
lackw
ellP
ublish
ers2001
Male manual full-time employees
Tmcv 0.134 (8.48) 0.131 (4.07) 0.149 (8.79) 0.174 (4.87) 0.150 (8.82) 0.174 (4.89) 0.153 (8.76) 0.177 (4.91)
Ntmcv 0.071 (3.81) 0.117 (3.52) 0.082 (3.96) 0.143 (3.61) 0.082 (4.00) 0.145 (3.64) 0.084 (4.10) 0.143 (3.60)
Adj. R2 0.313 0.199 0.311 0.182 0.312 0.181 0.309 0.182
Cover 0.110 (7.85) 0.124 (4.88) 0.125 (8.23) 0.160 (5.53) 0.126 (8.27) 0.161 (5.56) 0.127 (8.24) 0.162 (5.56)
Adj. R2 0.310 0.199 0.308 0.182 0.309 0.181 0.307 0.182
Member 0.100 (6.99) 0.128 (4.16) 0.111 (7.15) 0.148 (4.25) 0.111 (7.17) 0.149 (4.26) 0.110 (6.93) 0.152 (4.30)
Adj. R2 0.307 0.196 0.304 0.176 0.304 0.175 0.301 0.176
Sample 2,865 2,865 2,404 2,404 2,402 2,402 2,341 2,341
Notes:aAdjusted R-squared in the table refers to within R-squared for ®xed-effects estimates.bSample sizes refer to unbalanced panel samples and asymptotic t-ratios are in parentheses.cmeA equals zero if the two membership question responses appear consistent.dmeB equals zero if the two membership question responses exclude membership of staff associations.
Does
mea
surem
ent
error
bia
s®xed
-effectsestim
ates
of
the
unio
nw
age
effect?451
#B
lackw
ellP
ublish
ers2001
samples across waves 1 to 5. As before, restricting the sample to exclude the
very small number of inconsistent (meA 6� 0) answers makes very little
difference. Restricting the sample to the stricter de®nition of union member-
ship (meB � 0) reduces the sample by more, and generally indicates that the
wage effects of formal trade unions are greater than those of employee
organisations under both the OLS and ®xed-effects estimators.
In summary, restricting changes in union status to those where an
accompanying employer and/or job change also occurred generally increased
the ®xed-effects estimates of the union wage effect. This result is consistent
with measurement error causing a downward bias to ®xed-effects estimates,
but has two caveats. Firstly, the observed changes in the magnitude of the
union wage effect estimate are relatively small compared to the standard
error. Secondly, it must be remembered that by restricting union changes in
an attempt to remove some of the potential misclassi®cation and misreporting
of union status, some true changes will also be excluded. For example,
recognition and de-recognition of a union for the purpose of pay bargaining
will take place over time and such changes may well have an impact on an
individual's wage between periods without an employer or job change having
to occur. The same argument holds for membership changes, particularly if
by joining (leaving) the union the individual takes the membership density
above (below) a critical point at the establishment.
Reducing measurement error through averaging
The ®nal method used in this paper to investigate the degree of measurement
error bias in the ®xed-effects estimates is reported in Table 5. This method
was used by Chowdhury & Nickell (1985), who showed that by averaging
across the union observations potential measurement error through mis-
reporting and misclassi®cation can be reduced. This is because measurement
error exhibits no serial correlation itself but the actual union variable does.
The measurement error bias falls because the variance of the averaged
measurement error falls by more than the variance of the averaged union
variable. The higher the serial correlation between the true union status
across periods, the greater the relative change in the variance of the averaged
measurement error and union variable.22
In Table 5, the cross-section OLS and ®xed-effects estimates are shown
for the balanced panel sample across waves 1 to 6.23 A comparison with the
22Estimates of the serial correlation coef®cient for this balanced sample across waves 1 to 6 forthe female employees and male manual full-time employees were 0.7295 and 0.8584 respectively.Both ®gures will be an understatement of the true serial correlation because of the measurementerror.
23The balanced panel was used so that the full three-year averages could be found.
452 Bulletin
# Blackwell Publishers 2001
®xed-effects estimates in column 1 (the original ®gures) clearly shows that
the three-year average estimate of the union wage effect is higher for both the
female and male manual full-time employee samples. The male estimate
increases by a particularly large margin that may partly be due to the small
sample size. If it is true that the measurement error in the union variable
decreases as a longer period is used to calculate the average, one would
expect the panel estimate of the union membership wage effect to decrease as
the average becomes shorter. The results for the two-year average in Table 5
appear to con®rm this.24
To summarize, reducing measurement error by taking averages provides
TABLE 5
Union Wage Effect Estimates with Union Status Measurement Error Reduced Through
Averaging
Actual variables
2 year averages
(1991±1992),
(1993±1994) and
(1995±1996)
3 year averages
(1991±1993) and
(1994±1996)
OLS
Fixed-
effects OLS
Fixed-
effects OLS
Fixed-
effects
Waves 1-6
Female employees
Member V 0.088
(5.63)
0.024
(1.82)
0.101
(4.44)
0.049
(2.43)
0.106
(3.71)
0.065
(2.23)
Adj. R2 0.487 0.229 0.535 0.349 0.555 0.444
No. of observations 3,294 1,647 1,098
No. of individuals 549 549 549
Male manual full-time
employees
Member V 0.104
(4.24)
0.050
(1.49)
0.102
(3.23)
0.076
(1.69)
0.121
(3.10)
0.251
(3.44)
Adj. R2 0.265 0.220 0.321 0.360 0.347 0.482
No. of observations 960 480 320
No. of individuals 160 160 160
Notes:aAdjusted R-squared in the table refers to within R-squared for ®xed-effects estimates.bSample sizes refer to balanced panel samples and asymptotic t-ratios are in parentheses.
24These ®gures compare well with the estimates reported in Chowdhury & Nickell (1985) wherethe original ®xed-effects estimate of 0.100 for union membership increased to 0.145 (t-ratio 2.0)with a two-period ®xed-effects estimate using a three-year average. The union membership wageeffect increased further to 0.184 (t-ratio 3.0) when a four-year average was used.
Does measurement error bias ®xed-effects estimates of the union wage effect? 453
# Blackwell Publishers 2001
further evidence that measurement error in the union status variable causes a
downward bias in the ®xed-effects estimates. Averaging decreased the meas-
urement error and increased the returns to union status. The longer the period
over which the average was taken, the greater the reduction in bias caused by
measurement error.
V. Conclusions
This paper investigated the impact of estimating the union wage effect
(variously de®ned) for female employees and male manual full-time employ-
ees under cross-section and panel estimators, with data from the British
Household Panel Survey, waves 1 to 6. The union membership (member V)
wage effect is estimated as 0.098 under both OLS and between-effects
estimators for female employees across waves 1 to 6, the equivalent estimates
for the male manual full-time employees being 0.116 and 0.117. Using union
membership conditional upon coverage (tmcv) instead raises the estimate for
women, but lowers it for men.
Fixed-effects estimates of the union membership (member V) wage effect
(across waves 1±6) were approximately half the cross-section estimates in
both the female and male samples. Equivalent comparisons of the union wage
effect estimates of membership (conditional upon coverage) across waves 1,
5 and 6, show similar reductions for the male manual full-time employees,
but a slight increase for female employees. These results appear consistent
with previous research (Blanch¯ower (1997), Hildreth (1999)) using the
BHPS and are generally in line with union wage effect estimates in the
British literature of between 3 and 19 percent (see Booth (1995)). Union
wage effect estimates presented here (across different sample and estimators)
range between 4 and 15 percent (approximately), where union status is
de®ned as coverage, membership or membership conditional upon coverage.
The relative magnitudes of the cross-section and ®xed-effects estimates of
the union wage effect would appear to suggest that cross-section estimates
are upwardly biased. However two points need to be made. Firstly, the extent
to which cross-section estimates can be argued to be biased by unobserved
heterogeneity, through comparisons with ®xed-effects estimates, depends on
the superiority of the ®xed-effects estimates. If the ®xed-effects estimates are
themselves downwardly biased by measurement error, the divergence be-
tween the two estimates will be overstated, thus leading to inaccurate conclu-
sions concerning the degree of bias in cross-section estimates. Secondly, the
degree to which the panel estimates are smaller than the cross-section varies
across samples and union de®nitions.
The potential importance of measurement error in biasing ®xed-effects
estimates should not be underestimated as ®xed-effects estimates rely cru-
454 Bulletin
# Blackwell Publishers 2001
cially on changes in union status. Even a relatively small amount of measure-
ment error can have a considerable impact on the ®xed-effects estimates. Two
methods used to reduce the measurement error seemed to con®rm that ®xed-
effects estimates were biased downwards. Firstly, reducing the measurement
error through averages decreases the measurement error, thereby increasing
estimates of the union wage effect. Secondly, restricting a change in union
status to those with an accompanying employer change generally increases
the returns to union status under the ®xed-effects estimator. Finally, it was
found that formal trade unions have a larger impact on the wage than other
employee organizations (such as staff associations).
To conclude, panel estimates of the union wage effect have advantages
over cross-section estimates, which are likely to suffer from unobserved
heterogeneity bias. However, panel estimation also has disadvantages, most
importantly the problem of measurement error in the union status variable.
This will cause a downward bias in ®xed-effects estimates, thus overstating
the divergence of the cross-section and ®xed-effects estimates of the union
wage effect. As in the US study by Freeman (1984), there is evidence for the
British labour market in the 1990s, that the cross-section and ®xed-effects
estimates `bound the true impact of unionism' (pp. 24).
Date of Receipt of Final Manuscript: May 2001.
References
Andrews, M. J. Bell, D. and Upward, R. (1998a). `Union coverage differentials: Some
estimates for Britain using the New Earnings Survey Panel Data Set', BULLETIN, Vol. 60,
pp. 47±77.
Andrews, M. J. Stewart, M. B. Swaf®eld, J. K. and Upward, R. (1998b). `The estimation of
union wage differentials and the impact of methodological choices', Labour Economics,
Vol. 5, pp. 449±74.
Blanch¯ower, D. G. (1997). Changes in time in union relative wage effects in Great Britain
and the United States. The labour market consequence of technical and structural change
discussion paper no. 15, February. Oxford: Institute of Economics and Statistics, University
of Oxford.
Booth, A. L. (1995). The Economics of the Trade Union, Cambridge University Press,
Cambridge.
Card, D. (1996). `The effect of unions on the structure of wages: A longitudinal analysis',
Econometrica, Vol. 64, pp. 957±79.
Chowdhury, G. and Nickell, S. J. (1985). `Hourly earnings in the United States: Another look
at unionization, schooling, sickness and unemployment using PSID data', Journal of Labor
Economics, Vol. 5, pp. 38±69.
Freeman, R. B. (1984). `Longitudinal analyses of the effects of trade unions,' Journal of Labor
Economics, Vol. 2, pp. 1±26.
Hausman, J. (1978). `Speci®cation tests in econometrics,' Econometrica, Vol. 46, pp. 1251±
71.
Does measurement error bias ®xed-effects estimates of the union wage effect? 455
# Blackwell Publishers 2001
Hildreth, A. (1999). `What has happened to the union wage differential in Britain in the
1990's?' BULLETIN, Vol. 61, pp. 5±31.
Jakubson, G. (1991). `Estimation and the testing of the union wage effect using panel data',
Review of Economic Studies, Vol. 58, pp. 971±91.
Lewis, H. G. (1986). Union Relative Wage Effects: A Survey, University of Chicago Press,
Chicago.
Mellow, W. (1981). `Unionism and wages: A longitudinal analyses', Review of Economics and
Statistics, Vol. 63, pp. 43±52.
Mincer, J. (1983). `Union effects: wages, turnover and job training', in Reid, J. D. Jr (ed.) New
Approaches to Labor Unions (supplement no. 2 to Ehrenberg, R. G. (ed.) Research in Labor
Economics ). JAI Press Inc., Greenwich, Connecticut.
Oswald, A. and Walker, I. (1993). Labour supply, contract theory, and unions. University of
Keele, mimeo, November.
Stewart, M. B. and Swaf®eld, J. K. (1997). `Constraints on the desired hours of work of British
men', Economic Journal, Vol. 107, pp. 520±35.
Swaf®eld, J. K. (1998) `Wage differentials in the 1990s: Estimates of employer tenure, union
status and gender wage effects and modelling issues in estimation', September, Ph.D. thesis,
Department of Economics, University of Warwick, UK.
Appendix 1
Variables and sample means
TABLE A.1
De®nition Waves 1, 5 & 6 Waves 1±6
Female
Male
manual
full-time Female
Male
manual
full-time
Log of gross average hourly wage: weekly wage
divided by usual paid hours (basic plus overtime)
1.657 1.686 1.611 1.657
Union membership (employment section): `member' 0.356 0.466 ± ±
Union coverage: `cover' 0.536 0.557 ± ±
Covered union member: `tmcv' 0.345 0.444 ± ±
Covered non±member: `ntmcv' 0.191 0.112 ± ±
Union membership (values and opinions section):
`member V'
0.309 0.448 0.270 0.436
Union membership density at 2 digit industry level
(member)
0.382 0.340 ± ±
Union membership density at 2 digit industry level
(member V)
0.337 0.320 0.314 0.310
Full-time employee dummy 0.633 1.000 0.623 1.000
Public sector employee dummy 0.368 0.136 0.359 0.138
Regional price index (log) 0.008 ÿ0.010 0.006 ÿ0.012
Employer tenure in years 5.966 7.376 5.703 7.437
Firm size base group (employees ,25) 0.384 0.275 0.400 0.273
Firm size dummy (employees 25±99) 0.261 0.268 0.254 0.272
Firm size dummy (employees 100±499) 0.215 0.289 0.209 0.293
456 Bulletin
# Blackwell Publishers 2001
TABLE A.1
(continued)
De®nition Waves 1, 5 & 6 Waves 1±6
Female
Male
manual
full-time Female
Male
manual
full-time
Firm size dummy (employees 500�) 0.140 0.168 0.137 0.162
Social-economic group (base): Intermediate
non-manual
0.699 0.000 0.696 0.000
Social-economic group: Professional, manager or
employer
0.128 0.000 0.123 0.000
Social-economic group: Forman or skilled manual 0.039 0.654 0.039 0.666
Social-economic group: Semi-skilled manual 0.080 0.267 0.080 0.259
Social-economic group: Unskilled 0.049 0.041 0.057 0.045
Social-economic group: Agricultural worker 0.005 0.038 0.005 0.030
Quali®cation dummy, 1 if has any quali®cations
zero otherwise
0.837 0.720 0.817 0.705
Training dummy, 1 if had training in last year zero
otherwise
0.389 0.268 0.362 0.256
Age last left full-time education 17.864 16.530 17.764 16.486
Potential labour market experience de®ned as age last
left education minus current age (banded within
14 and 24), linear spline for 0 to 4 years, 5 to 9
years, 10 to 19 years and 20 plus years
20.573 21.614 20.682 21.353
Head of household dummy, 1 if not head zero
otherwise
0.778 0.193 0.783 0.209
Health dummy, 1 if bad zero otherwise 0.046 0.030 0.049 0.033
Married dummy, 1 if married or living as a couple
zero otherwise
0.750 0.750 0.749 0.746
Sample 3,457 1,220 8,673 3,187
Does measurement error bias ®xed-effects estimates of the union wage effect? 457
# Blackwell Publishers 2001
Recommended