does measurement error bias fixed-effects estimates of...

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 '.

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# 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


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.

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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.



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

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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


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.



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.

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(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.



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.

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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


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).



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


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.



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

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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

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bia

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of

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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


®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.



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


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.



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). Èstimation 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). Ùnionism and wages: A longitudinal analyses', Review of Economics and

Statistics, Vol. 63, pp. 43±52.

Mincer, J. (1983). Ùnion 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


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



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