Does Wage Discrimination Against Women Really Exist?
Laure Dutoit and Jean-Christian Lambelet
With the collaboration of José Anson1
1. Conceptual and Technical Problems
1.1. Two Intriguing Examples
Investigations of the labor market in Switzerland as well as in many other countries all show
that average wages tend to be lower for women than for men. However, this observation does
not suffice, in and by itself, to establish the existence of gender-based wage discrimination
because the observed discrepancies in average wages could result from differences in productivity,2 themselves due to various factors such as unequal skills. Put differently, gender-based
wage discrimination exists in a market economy if – and only if – women (men) are paid lower salaries than men (women) for a given productivity level.
Controlling for productivity however runs into a number of conceptual and technical problems which are not always fully appreciated. The following example, due to Conway-Roberts
(1983), illustrates one such problem. The numbers in table 1 are fictitious and kept simple for
clarity’s sake.
Table 1
Employees in Firm X
Number of Men
Education
High School
College
Master
Total
Clerical
40
23
1
64
Professional
0
17
19
36
Number of Women
Type of Job
Total
Clerical
40
80
40
16
20
0
100
96
Professional
0
4
0
4
Total
80
20
0
100
It is noticed that women are assumed to have a lower average education than men: 80 percent
of women stopped at the high school level as against 40 percent of men; only 20 percent of
women have a college education while 40 percent of men do; no woman has a master degree
as against 20 percent of men. It is assumed that professional jobs are preferable to (pay more
than) clerical jobs and also that productivity is highly correlated with education.
A first way in which these data can be tested for gender-based wage discrimination is to calculate the distribution of jobs according to education levels – see table 2. The table must be
read horizontally as the percentages sum up to 100 percent in that direction. No discrimination
can be detected for all those who stopped at the high school level: 100 percent of men and
women in that category hold a clerical job. However, 42.5 percent of men with a college degree have a professional job as against only 20 percent of women in that category. Symmetri-
1
Department of Economics and Econometrics (DEEP), Ecole des HEC, University of Lausanne. This article is
based on a research paper presented, during the academic year 2000/2001, by Dutoit to an applied econometric
class supervised by Lambelet (professor) and Anson (assistant). Lambelet has reworked the paper so as to make
it suitable for publication and he has contributed some inputs of his own. The original French-language version
of this paper can be found under: http://www.hec.unil.ch/modmacro/. For their valuable help, particular thanks
are owed Enrico Bolzani, Jacques Huguenin, Christophe Kolodziejczyk, Alexander Mihailov, Délia Nilles, Antonio Fidalgo and Dominique Dutoit. The usual disclaimers apply.
2
"Productivity" is always taken here to mean marginal productivity.
2
cally, 80 percent of women with a college degree are confined to clerical jobs as against only
57.5 percent for men. The conclusion seems clear: firm X discriminates against women.3
Table 2
Firm X: Job Distribution According to Education Levels
Men
Education
High School
College
Master
Total
Clerical
100%
57.5%
5%
64%
Professional
0%
42.5%
95%
36%
Women
Type of Job
Total
Clerical
100%
100%
80%
100%
0
100%
100%
96%
Professional
0%
20%
0
4%
Total
100%
100%
100%
A second way to test for discrimination is to examine the distribution of educational levels
according to the type of job – see table 3.4
Table 3
Firm X: Distribution of Educational Levels According to Type of Job
Men
Education
High School
College
Master
Total
Clerical
62.5%
35.9%
1.6%
100%
Professional
0%
47.2%
52.8%
100%
Women
Type of Job
Total
Clerical
40%
83.3%
40%
16.7%
20%
0%
100%
100%
Professional
0%
100%
0%
100%
Total
80%
100%
0%
100%
The table must now be read in the vertical sense. No discrimination can be detected among
employees who hold a professional job: no one in that category – man or woman – has
stopped at the high school level. However, 16.7 percent of women with a clerical job have
gone to college as against fully 35.9 percent of men, while 83.3 percent of women in that type
of job stopped at high school level as opposed to 62.5 percent of men. Symmetrically, only
47.2 percent of men with a college degree hold a professional job as against 100 percent of
women. The conclusion is as “clear” as previously, but it is just the opposite one: firm X discriminates against men. I.e. for the same type of job, men are required to have a higher education level. We shall see that, depending on the way in which one looks at the wage discrimination issue, conclusions just as contradictory are also reached when actual Swiss data are used.
The second example, due to Weisberg-Tomberlin (1982), is another illustration of the problems one can face when examining ex post whether an employer has been discriminating in
his hiring policy. In the authors’ own words:
(…) Suppose a company wishes to select six individuals for a particular position. There are ten
males and ten females available. They are all scored on a test that has been validated as a perfect
predictor of future productivity, with the following results:
Males: 40, 50, 60, 60, 70, 75, 80, 90, 95, 95
Females: 30, 35, 55, 60, 60, 75, 75, 75, 85, 90
Then, if the employer selects on the basis of this index, he will choose the top four men and the
top two women to obtain:
Selected Group: 80(M), 85(F), 90(M), 90(F), 95(M), 95(M)
3
4
It will be seen that the classification of table 2 corresponds to the “direct regression” case.
The classification in table 3 is akin to the “reverse regression” case – see below.
2
3
Note that although the requirements for men and women are identical, the distribution of qualifications will differ between the males and females selected. In particular, the average level of Q
[the test scores] for males selected is 90.0, while that for women is 87.5.
Does this represent discrimination against males, who seem after the fact to have had the more
significant standards applied?5 Clearly not. It simply represents the application of a nondiscriminatory rule where the marginal distributions of the two groups differ. The conditional
probability of Q given S [salary] is determined not only by the employer's requirements, but also
by the pre-existing population distribution for the groups.6
These two examples show that the probability of holding or getting a certain job, given one’s
productivity level as measured by skills, depends not only on the employer’s behavior, but
also on the pre-existing distribution of skills. Note however that in the first example the observed variables are all qualitative (or “categorical”): two types of jobs and three levels of
education are considered. In the second example, the test scores are measured by a (nearly)
continuous variable, but the question is whether a candidate will be hired or not, i.e. a binary
qualitative choice.
Now suppose that in both examples individual productivity and wage levels could be measured accurately and on continuous scales. Testing for discrimination would then be a straightforward matter and the results would not depend on any pre-existing distributions. However,
(marginal) productivity cannot be measured directly, so that all studies have to fall back on
indirect indicators or attributes, some of which at least are qualitative.7 It is then quite possible that the testing procedure will run into the type of problem illustrated by the two examples
and that contradictory and/or spurious conclusions could emerge depending on the preexisting distributions and on the way the testing procedure is run.
1.2 Direct vs. Reverse Regressions8
Most but not all econometric investigations of the wage discrimination issue draw on Jacob
Mincer’s human capital theory and hence estimate (generally by OLS, with a cross-section
sample and subject to minor variations) an earning equation of the following type, which is
conventionally called the “direct regression”:
log (Wagei) =  +  Qualificationi +  Sexi + i
(1)
“Wagei” is individual i's labor income. “Qualificationi” is a vector of i’s attributes – such as
education – serving as a proxy for (unobservable) productivity, where at least some attributes
are qualitative. The binary variable “Sexi” indicates i's gender (0 = male, 1 = female) and i is
an error term.9
The  parameter identifies discrimination, its direction and its size. If it is not significantly
different from 0, then no discrimination can be detected in the sample. If it is significantly
different from 0 and negative, there is evidence of discrimination against women and if it is
significantly positive, there is evidence of discrimination against men.
Equation (1) seems straightforward enough, but it is not always realized that it rests on one of
two possible ‘scenarios’ regarding the employers’ typical hiring behavior. In this first scenar5
It would of course be easy to construct an analogous example showing apparent discrimination against women.
Note that the argument is based on average wages whereas it would also be necessary to examine the other
moments of the distribution.
7
The basic problem thus is that that the underlying ‘true’ variables (wages, productivities) are continuous or
nearly so, whereas the available data are often made up of qualitative variables.
8
For a general discussion of this issue, see Maddala (1992, 459-61) and Maddala (2001, 449-51).
9
Most studies use the natural logarithm of the wage because this simplifies the interpretation of the  and  coefficients (they cans be viewed as rates of return).
6
3
4
io, employers examine a candidate's qualification and accurately assess her/his productivity.10
In a second step, they decide whether or not to hire the candidate and, if so, assign her/him to
a job that matches her/his skills. Therefore, in that case, qualification is considered as given
and it determines the job and the related wage.11
In a second scenario, employers first define a job and then search for a candidate whose qualification matches the job. Thus, in this second case, the required qualification and the suitable
candidate are determined by the job and its related wage, which is considered as given and is
supposed to be measured accurately. The corresponding equation, generally called the “reverse regression”, takes the form:
Qualificationi = ’ + ’ log (Wagei) + ’ Sexi + ’i
(2)
The two scenarios and the associated equations imply a different direction of causation.
Whether to use (1) or (2) thus requires a close examination of the employers’ actual hiring
behavior. If this is not done, trouble may ensue and a wrong conclusion could be reached
about the existence and the direction of wage discrimination. Suppose, for example, that the
second scenario and hence equation (2) apply in the real world, but that equation (1) is mistakenly used. As is well known, the estimated coefficients of (1) will not satisfy the condition
/ = – ’;12 in other words, ’, the discrimination coefficient in the “correct” equation, cannot
be derived from the estimation results for (1). This is illustrated by graph 1 in the general Y-X
case.
Graph 1
Y
Regression of X on Y
Bisector
Regression of Y on X
X
Suppose that, in this graph, the absence of discrimination corresponds to the slope of the bisector, a flatter (steeper) slope indicating discrimination against women (men). Suppose further that the employers’ actual behavior is such that one should regress X on Y (reverse regression), but that Y is mistakenly regressed on X (direct regression). The conclusion would
then be that there is discrimination against women whereas the opposite would be true.
Actual studies confirm this possibility. Thus, Conway-Roberts (1983) found, when using direct regression, significant wage discrimination against women in the USA. The reverse regression, however, revealed no evidence of discrimination at all. In another study by AbowdAbowd-Killingsworth (1983), who compared wages for whites and for members of several
other ethnic groups in the USA, direct regression indicated discrimination in favor of whites
while reverse regression pointed to discrimination against them.
To complicate things further, it is of course possible that, in the real economy, some employers in certain segments of the labor market behave according to the first scenario and some, in
other segments, according to the second scenario. Using a general sample drawn from the
10
I.e. it is assumed that there are no measurement errors when assessing productivity.
There is no need to worry about what happens after the candidate has been hired: her/his productivity has been
measured accurately.
12
Unless  happens to be equal to one. This could transpire by accident, but is unlikely because the “Qualification” variable is, at best, a transform of the true “Productivity” variable, about which more below.
11
4
5
entire labor market would then be inappropriate and might lead to spurious results, no matter
whether the direct or the reverse regression is used.
At the bottom of the issue discussed in this section (and in the next one too) lies the fact that
the fundamental microeconomic proposition involved takes the form of an equilibrium condition, i.e. the following relation:
Wagei = Productivityi ,13
(3)
which could just as well be written
Productivityi = Wagei .
(4)
If this relation holds for both men and women, there is no discrimination. Econometric methods such as OLS are however designed to estimate functions, but not relations like (3)-(4). To
repeat, moving from the underlying relation to an equation that can be estimated requires a
close examination of the employers’ actual hiring behavior to ascertain the direction of causation. Oftentimes this is not done. If the direction of causality is not known, one solution is to
run both a direct and a reverse regression so as to get two “bounds” around the true value of
the discrimination coefficient, one bound coming from the direct regression and the other
from the reverse regression.14
1.3 Error-in-Data
In the preceding, the explanatory variable in both the direct and the reverse regressions (qualification and wage, respectively) was assumed to be measured accurately. This is however a
strong assumption. As mentioned, individual marginal productivity cannot be measured directly and the vector of qualifications used instead can be a poor proxy. As to wages, the observed numbers could also suffer from significant measurement error – think of fringe benefits, perks, pension fund arrangements, stock options and other bonuses, jobs in the underground economy, etc.
This raises an additional problem besides the one discussed in the previous section. Suppose,
rather unrealistically, that some way has been found to measure marginal productivity directly. Furthermore, suppose that the observed data for individual productivities and wages are
equilibrium values or at least sufficiently close to equilibrium values (in itself a strong assumption).15 If both series were completely error free, no formal testing would be necessary:
in the absence of discrimination, the two series should be identical. If productivities are measured accurately but not wages, then one should use a direct regression equation analogous to
(1) and estimate it by OLS. If wages are error free, but not productivities, then it should be a
reverse regression equation analogous to (2), also to be estimated by OLS. See Goldberger
(1984) for further developments. In the real world, it could well be that wages are measured
with greater accuracy than the productivity proxies, which would point to reverse regression
as the better – or least bad – approach.16
Orthogonal distance regression (ODR) rather than OLS would seem an obvious choice when
trying to estimate a relation such as an equilibrium condition and when all variables suffer
from significant measurement errors. ODR appears to be quite popular in medicine and engineering, where it is often advertised as a method to sidestep the error-in-all-variables problem.
13
Of course, it has to be the real wage, but nominal and real wages are identical in a cross-section context.
Maddala (2001, 71-75, 449-51). Note that the estimated bounds are not comparable to a confidence interval
since they themselves have standard errors; ibid. 445.
15
Under these conditions, the issue discussed in the previous section would not arise.
16
As argued by Conway-Roberts, 1983, 1984. Other econometricians adduce various reasons against the use of
reverse regression – see Ferber-Green (1984), Greene (1984), Michelson-Blattenberger (1984) and Miller
(1984).
14
5
6
This is however true in a limited sense only as it turns out that the ratio of the error variances
must be supplied extraneously.17 Failing that, orthogonal estimators have infinite higher moments18 (at least in the case of linear models19), so that no hypothesis testing can be done and
no confidence intervals can be constructed.
As econometric textbooks tell us,20 the error-in-data problem calls for another estimation
method than OLS, e.g. instrumental variables (IV). In practice it is however generally hard to
find valid instrumental variables, i.e. instruments that are both truly exogenous and correlated
with the explanatory variables that suffer from measurement error. Moreover the choice of
instruments is in any case arbitrary in a single-equation context. Finally, IV estimators guarantee consistency only.
1.4 Different Parameters for Men and Women
Another problem stems from the fact that the parameters of some explanatory variables need
not necessarily be the same for men and women. Let us illustrate this by an example. Consider a direct regression which includes the age of the individual among its explanatory variables. As will be discussed below, a rational and non-discriminating employer might very well
assess the (future) productivity of a young man differently from that of a young woman with
identical attributes. The coefficient of the variables linked to productivity could therefore differ according to the individual's gender.
To deal with this possibility, Oaxaca (1973) and Blinder (1973) propose a two-step method.21
First, two regressions – one for men only and one for women only – are estimated. In a second step, the computed coefficients of the two regressions are compared and the differences
between them are decomposed into two parts: a first one due to the difference in the mean
values of the explanatory variables and a second one due to discrimination.
1.5 Selection Bias22
The last difficulty comes from a possible selection bias in the sample. When, in a direct regression for example, wages are regressed on the explanatory variables, unemployed and nonworking individuals are not included in the sample because they do not receive any wage.
This lack of earning may however result from their choosing not to work (auto-selection): the
wage they require – their reservation wage – is higher than the salary offered by the employer
and they decline the job offer. Because these people are not included in the sample, the latter
may therefore not be representative of the whole population. These missing observations may
– but need not necessarily – lead to a selection bias. Graph 2 illustrates the case where there
will be a bias.
The white dots represent unobservable wages and the black ones stand for observed wages. If
all dots could be observed (i.e. if there were no selection bias), the real regression line would
be the plain one. If the sample does not include the white dots, the dotted line will result from
the direct regression and it is clear that, because of selection bias, the conclusion about discrimination would be incorrect. To solve this problem, Heckman (1979) has proposed the
following correction method: a first step consists in estimating the probability that an individual – employed, unemployed or non-working – participates in the labor market. A second step
17
For example, see Ammann-Ness (1988).
See Anderson (1976, 1984) as quoted in Boggs et al. (1988, 172).
19
See Boggs-Rogers (1990).
20
E.g. Maddala (1992, 461-4).
21
A very clear exposition of this method can be found in Flückiger-Ramirez (2000).
22
This problem has become well known by now. We nevertheless discuss it briefly for the benefit of those who
might not be acquainted with it.
18
6
7
is to include this estimated probability in the regression as an extra explanatory variable. All
the available information is then used and the possibility of a selection bias is allowed for.
Graph 2
Wage
Explanatory variable
Summing up the preceding sections, it is clear that testing for wage discrimination is not a
straightforward matter of running a few regressions, but that all the problems discussed above
must be allowed for. This we have done for Switzerland and our results will be presented and
discussed below, where it will be seen that conflicting results emerge depending on the approach used, some results pointing to significant wage discrimination against women and
some to equally significant wage discrimination against men. Overall, the conclusion is that
the general issue remains open and, more specifically, that an absence of gender-based wage
discrimination cannot – as yet – be ruled out. This may come as a shock to many as it flies in
the face of current conventional (politically correct) wisdom. Not wishing to be misunderstood or misjudged, we therefore deem it necessary to insert, at this point, two sections discussing the general issue of wage discrimination from a theoretical as well as a normativeethical standpoint, the idea being to prepare the ground for an interpretation of our results.
1.6 Wage Discrimination and the Market Economy
It may be worthwhile pondering the fundamental question whether wage discrimination as a
general phenomenon (including discrimination based on criteria other than gender) is compatible with a “properly functioning” market economy, i.e. an economy where markets and particularly the labor market by and large conform to the competitive model.
Let us consider a market-based but politically illiberal society – e.g. South Africa under
apartheid or much of the American South till not so long ago – where employers share a
strong prejudice against a certain group of employees, such as black people, whom they consider to be inferior. Making up a big labor-market cartel, they might then pay black people
less than their marginal productivity, keeping the difference for themselves.23 In such a situation, there is however a powerful economic incentive for employers to defect from the cartel:
replace costly white workers by cheap black ones with the same qualifications.24 This incentive becomes particularly strong when the economy is overheating and there is excess-demand
in the labor market. Race-based wage discrimination might therefore be expected to erode
more or less rapidly in a market economy, to the point, perhaps, where it will disappear alto23
Employers therefore collude to pay black people a fraction only of their productivity, a fraction the employers
have to agree upon explicitly or tacitly. This is why it makes sense to speak of a cartel. – On this see Becker
(1971).
24
Of course, an important aspect of racism in societies such as those mentioned is to keep black people underqualified, for example by barring them from higher education. Since not all whites are highly qualified, far from
it, there however is an important intersection between the two groups.
7
8
gether. This however ignores that, in societies of this type, employers are very likely to face
other “incentives” of a non-economic nature: those who would be tempted to defect might
very well expose themselves to insistent moral-political pressures or, quite possibly, to nasty
physical ones. And, depending on how deeply and widely racist attitudes are rooted in society,
these non-economic pressures might be strong enough to permanently offset the economic
incentive to defect.25 Reasoning and the historical record thus suggest that race-based wage
discrimination can indeed exist for a long time in an illiberal market economy.26
What about a cartel aiming at wage discrimination against women? A first thing to notice in
this respect is that non-economic pressures of the type just mentioned would seem rather less
likely in a society free of racial prejudice, but where employers are colluding against women
for some reason (to be discussed in the next paragraph). Gender-based wage discrimination
might therefore seem more likely to erode over time in a market economy because of the economic incentive to defect, i.e. replace costly male labor by cheaper female labor with the
same qualifications.
Historically speaking, collusion aimed at gender-based wage discrimination may have come
initially into existent for ethically more justifiable reasons than racial prejudice. Thus, no official social security system coupled with more or less extensive income redistribution existed
in Switzerland before the late 1940s–early 1950s. In those times, the widely accepted social
standard for women was to get married, stay at home and take care of the children and the
household, while that for men was to work outside the household and to provide for the entire
family.27 The relatively few women who were active on the labor market usually did not – or
did not yet – have children and a family to take care of. Therefore, according to a view quite
generally accepted at the times, it was considered ethically and socially appropriate to pay
male employees more than females ones with the same job and the same qualifications. This
attitude was however not grounded in some crude sexism against women, but on a notion of
redistributive justice which, in the absence of an official social security system, was implemented privately, i.e. by collusion among employers.28 If men were paid more and women
less than their respective marginal productivity, the one more or less compensating the other,
this formally discriminatory system was also – unlike one based on racial criteria – devoid of
any exploitative element, although this aspect would bear being investigated more closely.
Then, starting some time around World War II, an extensive official social system was progressively put in place and prevailing social attitudes changed more or less pari passu,29 the
25
One might be tempted to argue that, to the extent that employers find themselves in a prisoner-dilemma type of
situation and that the game is played repeatedly, the non-defection outcome of the game could be a stable solution even in the absence of non-economic pressures. The number of players is however very large in this context
and there probably are severe information problems. Therefore, an analysis based on game theory does not appear to be appropriate.
26
After all, official apartheid lasted for almost half a century in South Africa and much of the American South
was basically racist till the 1960s. Historically speaking, racist societies have often been impelled to reform because of overwhelming outside pressure: intervention by the Federal Government in the American South, international pressure in the case of South Africa.
27
This was not only a matter of social standard, but was also linked to the state of “household technology”: before the advent of washing machines, central heating, frigidaires, vacuum cleaners, precooked food, disposable
diapers and so on, household keeping and child raising was a full time job.
28
This does not mean that this social system was perfectly fair and it very probably victimized some members of
society such as widowed or husbandless women with children to raise as well as women without private means
who wanted to deviate from the socially accepted norm. Symmetrically, men who remained bachelors or childless were likely to be advantaged.
29
Progress in household technology, such as that mentioned in the last but one footnote, surely played an important role too, as did increasing human capital accumulation by women. At the same time, general technological and economic progress made it feasible to implement an ever more extensive official social system.
8
9
expected result being a gradual disappearance of “old-fashioned” wage discrimination. However, social attitudes change slowly in general and it is quite possible that at least some elements of the old income reallocation system lasted for a fairly long time and that some relics
may still be extant even today. Nevertheless, all this goes to suggest that one should not be too
surprised by findings showing that there is no compelling evidence today pointing at wage
discrimination against women.
1.7 Wage Discrimination and Social Justice
In today’s economy some jobs require practically no qualifications and no training. For example, a cashier in a supermarket hardly needs to know how to count: she/he just puts items
on an optical reader, all subsequent operations are done by the cash register, which may even
automatically give back any change owed. If one should observe an earning gap between
males and females holding jobs of that type, it could only be the result of genuine wage discrimination.
At the other end of the spectrum, some jobs require high qualifications. Let us assume, by
way of illustration, that a bank wanting to hire a young financial analyst has a choice between
a young man and a young women, both being equally qualified, having just graduated from a
good business school. Even so, the bank will generally want to give extra training to its employee, on the job or otherwise and generally at the bank’s expense. For it, this is an investment in the employee’s human capital. Unlike physical capital, this type of capital will not,
however, become the property of the firm.30 Consequently, the bank cannot be sure that the
candidates for the job will stay with it long enough for its investment to be recouped. As a
result, it will hire the candidate with the highest probability that she/he will stay with it long
enough. In other words, the bank’s decision is partly a forward-looking one: unlike in the case
of a supermarket cashier, the financial analyst’s future productivity counts, as does the probability that her/his training-enhanced future performance will accrue to the firm during a sufficiently long time for the investment to be recouped.
Because of the biological fact that only women can give birth and that their presence beside
young children is generally deemed important, this probability will be lower, in the eyes of
the employer, for the young woman than for the young man. Hiring the former entails a specific and relatively high risk of an early departure due to one or several pregnancies. Thus, if
both the young woman and the young man must be paid the same salary, the employer will
prefer to hire the young man. Alternatively, it may choose to pay the young woman a lower
wage.31 The resulting wage differential will however not reflect gross gender-based discrimination and it should rather be viewed as a sort of insurance premium protecting the firm
against the higher probability that the young woman will quit “prematurely”.32
30
Or to a limited extent only. Thus, as a counterpart to the training, the bank may ask the employee to sign a
contract by which she/he agrees to stay with the firm for a specified period, commits herself/himself not to join a
competitor during a certain time in case she/he decides to leave the firm, pay a penalty if she/he nevertheless
does quit, etc. Because indenture and slavery are no longer considered acceptable, there are however severe legal
constraints to such contracts.
31
Still another possibility is to hire the young woman, but invest less in her subsequent training. A wage gap
would then open up between her and a young man with the same qualifications and hired at the same time, but
this gap would be due to increasingly divergent qualifications and not, therefore, to gender-based discrimination.
32
Against this, it is sometimes argued that young men must also be expected to absent themselves periodically
from their jobs due to military obligations. This prospect is particularly relevant in Switzerland where universal
male military service is the rule, the Swiss army being a citizens’ militia. However, past an initial training period
lasting four months, the military “refresher courses” last a couple of weeks only, i.e. they are far shorter than
maternity-related leaves. Moreover, these refresher courses can often be negotiated to take place at times that are
not too inconvenient for the employer.
9
10
Even though the (profit-maximizing) employer acts rationally when paying a lower wage to
the young woman so that no gross gender-based discrimination is involved, this does not
mean that all will be for the best in the best of non-sexist worlds. Women did not choose to be
of that gender. Neither are they responsible for the fact that they are the ones who give birth.
Hence, from an equal-opportunity standpoint, one should talk not of discrimination, but of
social injustice or nature-based inequality.
From an equal-opportunity viewpoint, this inequality should be corrected, which can be done
– and is generally done in most countries including Switzerland – through law by requiring
employers to pay men and women the same wage for the same job. This however creates an
incentive for employers to hire men rather than equally-qualified women. Correcting this hiring bias by administrative-judicial means is likely to run into severe implementation problems
related, among other things, to the notion of what exactly constitutes “equal qualifications”.33
Another approach than the legal-administrative route might therefore be preferable and should
at least be explored. During World War II, Swiss men of military age who were not mobilized, and hence who could go about their civilian jobs, were subject to a special levy on their
earnings, the proceeds of which were used to give financial compensation to mobilized men.
By analogy, one might consider a system other than the legal-administrative one, i.e. a system
under which an extra tax would be levied on the labor income of men aged less than 45 and
the proceeds given to firms who hire women in the same age bracket. Of course, this would
mean an extra administrative apparatus, not to mention still another levy on labor income, and
determining the modalities of the levy, such as its rate, would be no easy task. The question
therefore is which system – and there might be others besides these two – is the more efficient
and least costly one. But a cost there will be in any case if one wants to correct the unequal
chances of women.
2. Is There Really Wage Discrimination Against Women in Switzerland Today?
2.1 Previous Studies on Gender-based Wage Discrimination in Switzerland
The most recent study of gender-based wage discrimination in Switzerland (FlückigerRamirez 2000) emphasizes the differences in the mean wages of men and women and it highlights their evolution over time. The authors characterize the Swiss labor market according to
a variety of criteria (size of the firm, hierarchy, hours of work, field of activity, etc.) After
discussing a number of theories about wage discrimination, they proceed to an econometric
investigation. Applying the method of Oaxaca-Blinder, they conclude that there is significant
wage discrimination against women.
Older studies (Diekmann-Engelhardt 1994, Brüderl-Diekmann-Engelhardt 1993, Kugler
1988) approach wage discrimination through human capital theory. They make use of Heckmann’s correction for a possible selection bias and apply a wage gap decomposition procedure to the results of separate regressions for men and women, mostly with the help of the
Oaxaca-Blinder method. All these studies detect significant discrimination against women.
Bonjour and Gerfin (1997) and Luzzi-Silber (1998) raise doubts about the Oaxaca-Blinder
wage gap decomposition procedure and discuss some other methods.
2.2 Data Used for our Econometric Investigation
Our cross-sectional data set comes from the 1997 Swiss Labor Force Survey performed by the
Federal Statistical Office. This survey was published in 1998, being the most recent available.
It covers 16,000 individuals. However, the number of observations used in our study is smaller because, in some parts of our work, we do not include people who received no wages (the
33
This is quite apparent when, for example, a university professorship has to be filled.
10
11
unemployed and people not in the labor force).34 This reduces the data set to 9,922 observations. Moreover, some people did not answer all questions, i.e. the information about them is
not complete enough and these individuals must be excluded from the sample. 3,666 observations thus remain in the end – still a large enough sample.
The characteristics of our sample are the same as those in the first example at the beginning of
the paper, except that some variables are continuous or nearly so (e.g. wages and age). Many
more attributes are also available and will be made use of (marital status, place in the firm’s
hierarchy, etc.)35
In the following sections we limit ourselves to reporting and commenting the main results of
our investigation when using different approaches. The detailed results as well as various
technical matters and comments are all relegated to an appendix.
2.3. General Direct Regression36
This direct regression is akin to equation (1) above: using a sample including employed people only, the individuals’ wages are regressed on their attributes.37 With thirteen attributes, 53
percent of the wages’ cross-sectional variation is explained (adjusted R2=0.53), which is honorable in a cross-section context.
The most significant explanatory variable (t=24.3), with a positive impact on wages, is the
occupation rate,38 which is hardly surprising. The second most significant one is the education
level (t=14.5),39 which is not surprising either. It influences wages positively.
The following variables also have a positive and significant impact on wages: the firm's size40
(t=7.1), the individual's experience41 (5.2), her/his nationality42 (4.4), the specific sector in
which the firm is active43 (4.4), the type of contract the employee has44 (3.6) and the individual’s age45 (2.6).
34
Heckman's correction requires the whole sample, i.e. including the unemployed and people not in the labor
force – see below.
35
For a full list, see A.1 in the appendix.
36
See A.2 in the appendix, regression R1.
37
The estimations were done by OLS. As there were signs of heteroscedasticity, White's correction was applied
to most regressions.
38
The occupation rate is defined as the ratio of the number of hours worked weekly to the hours of work considered as normal in Switzerland (40 hours).
39
This discrete variable takes the following values in the survey: 1 = compulsory school or elementary formation; 2 = apprenticeship, professional school, general formation school or secondary school examination qualifying for entry to university; 3 = technical school; 4 = professional high school, technical high school or university. These values are arbitrary as there is no reason why someone with a university degree should be exactly
four times more productive than someone who has completed compulsory schooling only.
40
The bigger the firm, the more – ceteris paribus – it pays its employees: this could be due to economies of
scales and/or to greater market power.
41
This variable measures the number of years the individual has been in the labor market without any long interruption.
42
This discrete variable takes the following values: 1 = Swiss nationality; 0 = other nationalities. Does a positive
and significant sign mean discrimination against foreigners? Perhaps, but nationality could also be considered as
an indicator of stability.
43
This variable takes the value 1 if the firm is part of the tertiary sector and 0 otherwise. Its positive and significant parameter could reflect the higher profitability of firms in the tertiary sector – think of banks, for example.
This finding need not be constant in time and might reflect relative profitability at the time the survey was taken.
44
The contract is limited in time = 1; the contract is not limited in time = 0. A non-limited contract can be an
incentive for the employee to put more effort in the firm.
45
Age is measured in round years. The reason why this variable is only weakly significant may be that its relationship with wages is non-linear, probably following an inverted U-shape: in a first period in one’s active life,
accumulating experience prevails over the loss of energy, initiative and creativity coming with the years. In a
11
12
Non-significant explanatory variables (at the 1% level) include marital status46 (t=1.5), length
of service in the firm47 (1.6), the individual's place in the firm’s hierarchy48 (1.1) and the
broad economic sector (private, public) to which the firm belongs49 (0.9).
The coefficient of the "Sex" variable (0=male; 1=female) is negative and significant. Hence,
according to this general direct regression, women would appear to be victim of wage discrimination: ceteris paribus, they seem to be paid 16 percent less than men – no trivial gap.
2.4. Separate Direct Regressions50
Because some parameters might be different for men and for women as argued above, equation (1) is now estimated separately for each gender. The discrepancies between the two direct
regressions' coefficients are then analyzed by means of the Oaxaca-Blinder method.
The estimation results confirm that the impact of most explanatory variables can be different
depending on the gender of the individual – see the appendix. The decomposition method
shows that 29 percent of the total difference between men's and women's wages is not explained by differences in mean productivities and that this discrepancy is due to discrimination against women. However, some explanatory variables (the education level, for example)
reveal a discrimination against men. Nevertheless, the total difference indicates that overall
discrimination is against women.
2.5. General and Separate Reverse Regressions with Qualification Index51
In the previous regressions, we tested the hypothesis: for the same productivity level, do men
(or women) get a higher wage?
In this section, the converse hypothesis is tested: for a given wage level, what qualifications
or, more generally, what productivity is required from men and women? The estimated equations are therefore akin to (2).
Because the sample includes more than one qualification indicator, reverse regressions can be
computed in two different ways. In a first approach, the main results of which are given in this
section, a qualification index is created, to be regressed on wages and some other explanatory
variables not linked to productivity. I.e. from the set of explanatory variables used in the direct regressions, those variables are selected which are linked to productivity and which can
therefore be used meaningfully to construct the dependent variable in the reverse regressions.52 Then, using as weights those variables’ direct regression coefficients, a qualification
index is calculated.
second period, it would be the other way around. Consequently, age squared could also have been included in the
equation.
46
Non-continuous variable (1 = married; 0 = other).
47
Non-continuous variable (1 = 8 years in the firm or more; 0 = less than 8 years).
48
This discrete variable goes from 1 = senior executive to 9 = unskilled worker or employee.
49
This is interesting as it runs counter to a widely-held view whereby different wage policies are followed in the
public and the private sector.
50
See A.2 in the appendix, regressions R2, R3 and decomposition OB1.
51
See A.3 in the appendix.
52
For example, the firm's size cannot enter the construction of the dependent variable in a reverse regression: the
question "For the same wage, are men (or women) required to be part of a larger/smaller firm?" makes no sense.
The variables included in the constructed index are consequently the following ones: age, education level, length
of service, experience, place in the firm’s hierarchy, hours worked and kind of contract. Besides wages and gender, the following variables are retained as explanatory variables: the firm’s size, the general and specific economic sector in which the firm is active, the individual’s marital status and her nationality. In the case of the
latter two variables, it is arguable whether they should be included in the index or not. The view taken here is
that marital status and nationality are not linked to productivity and must therefore be excluded from the index.
12
13
This first approach may however run into the following problem. Suppose that equation (2),
i.e. the reverse regression, is the “true” one – see the above discussion about the direction of
causation and the employers’ actual hiring behavior. Then, the coefficients of the direct regression used as weights for the qualification index would be biased and so would the index.53
In a second approach, used in the next section, the selected qualification indicators are consequently regressed one by one on all other attributes, plus the variables not linked to productivity as well as wages and a gender dummy.
The inference we can draw from the general reverse regression using the first approach is discrimination against men.54 The "Sex" variable is negative and highly significant (t = –18.1):
for the same wage level, Swiss employers require men to be more qualified than women.
This result is verified by the gap decomposition procedure:55 37 percent of the difference in
mean qualifications between men and women cannot be explained by the differences in the
means of the explanatory variables for men and women and is attributed to discrimination
against men.
2.6. General and Separate Reverse Regressions with Alternative Dependent Variables56
In principle, seven productivity-linked attributes can be used as the dependent variable in as
many general and separate reverse regressions. However, among them, only three yield results
statistically robust enough to be worth being reported. A first reverse regression takes the education level as the dependent variable.57 Both the general estimation and the Oaxaca-Blinder
method show evidence of strong discrimination against men. When selecting the occupation
rate and years of service in the firm as the dependent variable, we get the same results. In the
last case, the degree of discrimination against men however turns out to be considerably
smaller.58
2.7. Heckman’s Correction59
To apply Heckman’s correction we include non-working people and the unemployed in the
sample. Since reverse regressions have no sense in this context, we re-estimate the general
direct regression as well as the separate direct regressions for men and women.
As it turns out, it is not necessary to apply Heckman’s correction to the male sub-sample: as
men’s probability of participating in the labor market is almost one, no selection bias can occur. In consequence, the direct regressions for men with and without the correction give practically the same results.60 As for women, their participation probability is however significantly smaller than one. Therefore, the differences between the two regressions, with and without
the correction, are significant and Heckman’s procedure is the relevant one.
With Heckman’s correction, the general direct regression with a sample including both men
and women points to discrimination against women, but the gender dummy is now significant
at the 10 percent level only. Moreover, the size of the discrimination effect against women is
reduced considerably: instead of being paid 16 percent less than men, the gap now amounts to
barely 4 percent. Finally, the separate (Oaxaca-Blinder) direct regressions with Heckman’s
correction now detect discrimination against men.
53
Maddala 2001, 451.
See R4 in the appendix.
55
See R5, R6 and OB2 in the appendix.
56
For more details, see A.4, A.5 and A.6 in the appendix.
57
See A.4 in the Appendix.
58
See A.5, A.6 in the Appendix.
59
For more details, see A.7 in the appendix.
60
For a comparison, see A.2 in the appendix, regression R3, and A.7, regression R18.
54
13
14
Other gender studies of the Swiss labor market support these findings. Diekmann-Engelhardt
(1994) similarly found that the probability of taking part in the labor market has a positive
statistical impact on wages. This means that the observed (and observable) earnings underestimate, in an econometric sense, the wages of women who work. Moreover, these authors and
Kugler (1988) show that the non-explained part of the differences in mean wages, i.e. the discriminatory element in the Oaxaca-Blinder method, becomes smaller when Heckman’s correction is applied.
3. Conclusion : Still an Open Issue
In view of these conflicting results, our overall conclusion can only be agnostic: given the
current state of knowledge and econometric techniques, there is no way of making a scientifically substantiated statement about the existence or non-existence of gender-based wage discrimination in Switzerland – or, at least, this is not possible with the sample and techniques
we have used. Put differently, the absence of such discrimination cannot be ruled out. This
possibility, shocking though it may seem to many, should not be rejected out of hand since
there are, as we have seen, strong a priori reasons to think that gender-based wage discrimination is not compatible with an efficient market economy.
In any case, the possible absence of wage discrimination would not mean that there are no
inequalities between genders. Because only women can give birth and because the welfare of
(very) young children requires their mother’s more or less continuous presence, the career
prospects of women tend to be significantly less than those of comparable men. Social justice
requires that this be compensated financially, i.e. the foregone income due to child bearing
and rearing should be made good, e.g. by an adequate maternity social insurance system. The
ceteris paribus lesser labor-market prospects of women should be – or, as the case may be,
must stay – corrected as much as feasible, be it by law of by some other possibly more efficient approaches. Finally, it should be made as easy as possible – by means such as inexpensive (subsidized) daycare centers in sufficient number – for women to have children while
pursuing a professional career.
A stationary population requires a fertility rate of about 2.1 (children per woman on average).
Since about 1975 this rate has fluctuated between 1.5 and 1.6 in Switzerland, down from 2.7
in 1960 and 2.1 in 1970.61 In other words, Switzerland’s population is no longer renewing
itself and, at the limit, the “Swiss species” will disappear – barring, that is, massive immigration, which would however raise difficult issues of its own. There can be little doubt that
Switzerland’s alarming demographic deficit is partly due to the facts and problems discussed
in this article. Presumably, there are also non-economic reasons (e.g. religious values) why
couples decide to have children or not and, if so, how many. But the demographic survival of
society as a whole is hardly ever taken into consideration, meaning that a significant externality is extant and must be corrected. Sweden’s recent experience shows that, given the appropriate policies, it is possible for women to participate fully in the labor market without its entailing a demographic deficit.
61
See Statistisches Jahrbuch der Schweiz 2002 / Annuaire statistique de la Suisse 2002, p. 39.
14
15
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16
17
APPENDIX
A.1. Explanatory Variables
Explanatory variables
Variables concerning the individual
Age
Marital Status
Nationality
Gender
Education level
Variables concerning the individual and the firm
Length of service
Type of contract
Experience
Position in the firm’s hierarchy
Occupation rate
Variables concerning the firm
Activity sector
Sector (private/public)
Firm's size
The nature of these explanatory variables in explained in various footnotes to the main text.
17
18
A.2 General and Separate Direct Regressions
Variables
Constant
Male & Female
Female
Male
R162
R2
R3
7.799*
7.746*
7.790*
(58.090)
Age
Education
0.004*
0.002
Ef
OB1
0.044
(47.738)
0.006*
0.199
-0.021
(2.552)
(0.596)
(5.226)
90.6%
9.4%
0.195*
0.218*
0.178*
-0.073
0.082
(14.470)
Sex
(33.790)
Df
(7.091)
(17.189)
46.9%
53.1%
0.074
0.008
90.0%
10.0%
-0.160*
(-5.580)
Marital status
0.034
(1.513)
Nationality
Occupation rate
0.098*
Length of service
Firm's size
Activity sector
Experience
Hierarchy
0.060
0.088*
(5.088)
0.128*
(1.689)
(4.554)
0.022*
0.020*
0.022*
(15.008)
0.198*
0.270*
(3.555)
(2.817)
0.035
0.130
(2.261)
-0.004
3.4%
0.139
0.453
23.5%
76.5%
-0.133
0.001
99.1%
0.9%
-0.018
0.002
(0.681)
90.9%
9.1%
0.002*
0.003*
0.001*
-0.063
0.006
(7.064)
(5.075)
(5.855)
91.3%
8.7%
0.054
0.013
96.6%
(1.408)
0.067*
0.062
(14.240)
0.129
(1.617)
0.072*
0.016
-0.013
55.0%
45.0%
0.019
0.030
39.0%
61.0%
(4.426)
(1.716)
(4.348)
0.153*
0.129*
0.160*
(5.225)
(2.565)
(6.646)
-0.001
-0.049
0.000
99.8%
0.2%
-0.062
0.000
99.9%
0.1%
0.004
(1.139)
Sector (private/public)
(-1.135)
(4.429)
(24.288)
Type of contract
-0.061
0.025
(0.940)
0.010
(1.523)
0.071
(1.303)
(-0.288)
-0.011
(-0.600)
Total difference
Adjusted R-squared
0.531
Log likelihood
-3061.656
* Significant at the 1% level
0.425
-1831.578
0.223
0.544
29.1%
70.9%
0.498
-759.054
In the “OB1” (Oaxaca-Blinder) columns, “Ef” is the part of the wage gap due to differences in
the attributes’ mean values and “Df” is the part due to discrimination. In other words, “Ef” is
“the value of the advantage in endowments possessed by the high-wage group [men in our
case] as evaluated by the high-wage group’s [men’s] wage equation” (i.e. evaluated according
to the coefficients of the men’s wage equation) and “Df” is “the difference between how the
high-wage [men’s] equation would value the characteristics of the low-wage group [women]
and how the low-wage [women’s] equation actually values them”.63
In this case, 29 percent of the total mean wage gap is due to the employer’s discriminating
behavior. In consequence, we can infer from this method that women suffer from wage discrimination. Some variables (education or type of contract, for example) show a discrimination against men (“Df” is negative).
62
63
R1 = Regression 1.
Blinder (1973).
18
19
A.3 Reverse Regressions with Qualification Index as Dependent Variable
Variables
Constant
Male & Female
Female
Male
R4
R5
R6
6.397*
7.009*
5.815*
(66.739)
Wage
0.407*
(50.129)
Sex
(9.862)
0.331*
(4.923)
Df
Ef
OB2
-1.194
(20.994)
0.443*
(17.319)
1.122
0.448
71.5%
28.5%
-0.244*
(-18.134)
Marital status
Nationality
-0.111*
-0.305*
0.042*
(-9.283)
(-8.318)
(3.597)
-0.099*
-0.000
-0.044
(-2.454)
Firm's size
Activity sector
Sector
0.000
(-3.606)
0.001*
(-0.021)
-0.000
0.171
-0.023
88.30%
11.70%
0.188
0.001
99.6%
0.4%
-0.044
0.006
87.9%
12.1%
0.023
0.036
39.3%
60.7%
(2.189)
(2.748)
(-0.997)
-0.053*
-0.069*
-0.042*
(-3.804)
(-3.053)
(-3.868)
0.010
0.012
0.014
0.001
(0.737)
(0.490)
(1.091)
Total difference
Adjusted R-squared
0.566
Log likelihood
-1414.816
* Significant at the 1% level
0.481
-909.030
-0.011
10.5%
89.5%
0.268
0.458
36.9%
63.1%
0.48
53.207
The general reverse regression as well as the separate reverse regressions, to which the gap
decomposition method is applied, show evidence of discrimination against men; the coefficient of the variable sex is negative (which means that being a woman ceteris paribus lowers
the required qualifications) and 36.9 percent of the difference in mean qualifications cannot
be explained by differences in mean attributes. A positive sign of “Df” means that men suffer
from discrimination, since the greater the coefficient in the reverse regression, the more qualifications do the employers require.
19
20
A.4 Reverse Regression with Education as Dependant Variable
Variables
Constant
Wage
Age
Male & Female
Female
Male
R7
R8
R9
-1.662
-0.310
-5.812*
(-2.464)
(-0.542)
(-9.543)
0.374*
0.215*
0.862*
(4.438)
(3.074)
0.000
(0.307)
Sex
-0.003
(-1.596)
Df
Ef
OB3
-0.658
0.152
-0.013
(12.623)
92.4%
0.000
6.468
0.871
88.1%
11.9%
-0.010
-0.005
66.1%
33.9%
(0.129)
7.6%
-0.248*
(-7.794)
Marital status
Nationality
Occupation rate
0.051
(0.250)
0.271*
0.222*
0.225*
0.007
-0.406
(5.894)
(3.494)
(3.703)
1.6%
98.4%
-0.005
-0.002
-0.016*
-1.032
(-6.618)
47.3%
52.7%
-0.207*
(-2.790)
Length of service
-0.108*
(-3.503)
Firm's size
Activity sector
Experience
0.001*
Sector
(-0.910)
-0.249
(-2.382)
-0.052
-0.173
1.150
0.072
0.164
(-1.691)
30.5%
69.5%
-0.141*
-0.032
(-1.148)
(-3.457)
59.4%
40.6%
0.001
0.001
-0.019
-0.024
44.5%
55.5%
(2.189)
0.170*
0.246*
-0.136
-0.076
(5.396)
(4.876)
(2.396)
64.0%
36.0%
-0.152*
-0.076
-0.287*
-0.132
(-5.199)
41.2%
58.8%
-0.015*
(-1.631)
0.088
0.056
0.031
(-2.502)
(-0.928)
64.6%
35.4%
0.021
0.029
0.032
0.056
-0.024
8.3%
91.7%
(0.690)
-0.007
0.189
(-2.592)
(0.674)
-0.020
(1.247)
0.022
(3.013)
(-4.107)
Hierarchy
0.010
(0.721)
(-2.169)
Type of contract
0.031
(1.737)
(0.786)
Total difference
Adjusted R-squared
0.153
Log likelihood
-4250.006
* Significant at the 1% level
0.092484
-1820.89
4.738
1.877
71.6%
28.4%
0.203
-2234.429
These results reveal a discrimination against men and in favor of women: the coefficient of
the variable "Sex" is negative and significant. The Oaxaca-Blinder method shows that no
more than 28.4 percent of the mean qualification gap is explained by differences in mean attributes. The remaining 71.6 percent can be related to discrimination. Hence, for the same
wage, employers discriminate against men who are required to have a higher qualification
level than the one required from a comparable women. However, we must be careful when
considering these results; all regressions have a low adjusted R2, which casts doubt on the
robustness of the estimations.
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21
A.5 Reverse Regression with the Occupation Rate as Dependent Variable
Variables
Constant
Wage
Age
Education
Male & Female
Female
Male
R10
R11
R12
-47.787
-26.612
-49.985*
(-1.996)
(-0.895)
(-3.942)
15.002*
13.152*
14.346*
11.933
14.499
(6.272)
(4.352)
(11.511)
45.1%
54.9%
-0.282*
-0.363*
-0.217*
(-8.604)
(-6.457)
(-7.116)
40.3%
-2.134*
-1.913
3.89
(-6.852)
0.33
0.67
7.398
0.111
-1.681
(2.510)
Sex
-1.090
(-0.971)
Df
Ef
OB4
-23.373
7.194
10.639
59.7%
-8.988*
(-7.632)
Marital status
-7.020*
Nationality
Type of contract
Length of service
Activity sector
Experience
Hierarchy
Sector
-0.203
(-0.443)
98.5%
1.5%
-4.778*
-7.348*
-2.025*
10.131
3.651
(-6.981)
(-5.258)
(-2.876)
73.5%
26.5%
-1.000
0.725
0.246
(-0.594)
(-0.366)
(-0.153)
74.6%
25.4%
0.685
0.023
1.029
0.358
(1.144)
Firm's size
-15.195*
(-9.007)
(-11.062)
0.007
-1.026
(0.020)
0.026
-0.261
(2.146)
69.3%
-0.009
-1.470
(0.941)
(1.957)
(-1.590)
-2.811*
-4.110*
-2.128*
(-6.114)
(-3.784)
(-5.244)
3.707*
4.620*
(3.525)
(3.177)
-0.025
-0.197
(-0.254)
(-1.042)
0.092
0.197
(0.150)
(0.175)
0.873
(1.247)
0.110
(1.252)
0.307
(0.619)
Total difference
Adjusted R-squared
0.536
Log likelihood
-15033.490
* Significant at the 1% level
0.491
-7229.551
-0.159
30.7%
0.368
80.0%
20.0%
1.705
1.832
48.2%
51.8%
-2.347
-0.573
80.4%
19.6%
1.310
73.6%
0.084
-0.470
26.4%
-0.230
26.7%
73.3%
11.736
33.804
25.8%
74.2%
0.362
-7213.642
According to these estimations, men are again discriminated against: the coefficient of the
“Sex” variable is significant and negative. This result is validated by the Oaxaca-Blinder
method: 25.8 percent of the difference in mean occupation rates is due to discrimination.
Therefore, for the same wage, the same education level and the same values for the other explanatory variables, men are asked to work more than women.
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22
A.6 Reverse Regression with Length of Service as Dependent Variable
Variables
Constant
Wage
Age
Male & Female
Female
Male
R13
R14
R15
-0.697*
-0.531*
-0.968*
(-6.106)
(-3.822)
(-4.109)
0.019
0.018
0.018
-0.437
0.001
0.018
(1.314)
(0.678)
5.5%
94.5%
0.013*
0.011*
0.015*
0.203
-0.723
-0.030*
(-3.514)
Sex
Ef
OB5
(1.537)
(18.103)
Education
Df
(11.183)
-0.015
(14.325)
21.9%
78.1%
-0.041*
-0.047
(-1.157)
(-3.422)
38.8%
0.075
61.2%
0.055
0.012
-0.021
-0.006
76.6%
23.4%
-0.027
(-1.706)
Marital status
0.040*
(2.679)
Nationality
0.023
(1.119)
Occupation rate
0.001
(1.174)
Type of contract
Firm's size
Activity sector
Experience
Hierarchy
0.076*
-0.010
(-0.319)
0.000
(0.020)
0.058
(0.552)
0.045
(1.615)
0.002
(2.206)
0.100*
0.104
56.2%
0.160
49.9%
0.040
-0.081
43.8%
-0.160
50.1%
-0.094
(2.927)
(1.570)
(2.767)
29.7%
70.3%
0.001*
0.001*
0.001*
-0.006
-0.042
(6.108)
(4.414)
(4.040)
11.7%
88.3%
-0.031
-0.043
-0.025
0.016
0.021
(-1.846)
(-1.480)
(-1.200)
42.9%
57.1%
0.335*
0.353*
0.314*
-0.025
-0.206
(21.931)
(16.907)
(14.011)
10.7%
89.3%
0.002
-0.004
0.007
0.048
(0.531)
Sector
(2.422)
0.023
(1.462)
(-0.972)
0.014
(0.641)
(1.613)
0.032
(1.463)
Total difference
Adjusted R-squared
0.307
Log likelihood
-1904.987
* Significant at the 1% level
0.310
-792.187
62.2%
0.014
36.5%
-0.029
37.8%
-0.024
63.5%
0.050
-1.252
3.8%
96.2%
0.288
-1096.165
The general regression (R13) suggests that there is discrimination against men. This result
must however be considered with care since it is significant at the 10 percent level only. The
gap decomposition method however detects (slight) discrimination against men: 3.8 percent
of the difference in mean length of service cannot be explained by difference in mean attributes.
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23
A.7 Heckman's Correction
Variables
Constant
Male & Female
Female
Male
R16
R17
R18
Equation 1: Dependent variable: Wages
8.334*
8.445*
7.787*
(98.227)
Age
0.022*
(23.071)
Education
0.072*
(5.614)
Sex
(57.454)
0.027*
(16.200)
0.020
(0.776)
Df
Ef
OB6
-0.658
(80.042)
0.006*
-1.034
-0.277
(4.334)
78.9%
21.1%
0.179*
(16.266)
0.291
47.1%
-0.326
52.9%
-0.039
(-1.700)
Marital status
0.015
(0.688)
Nationality
Occupation rate
Type of contract
0.091*
Firm's size
Activity sector
Experience
Hierarchy
0.098
0.090*
0.000
-0.049
(4.443)
0.4%
99.6%
0.128*
0.058
-0.231
(2.407)
(5.402)
0.019*
0.017*
0.022*
(44.314)
(26.439)
0.079
0.099
0.040
(1.586)
0.130*
(3.195)
Household's size
Sex
80.9%
7.3%
0.001*
0.002*
0.001*
-0.019
-0.051
(7.521)
(4.982)
(5.864)
27.3%
72.7%
0.096*
0.108*
0.072*
-0.031
-0.062
(5.480)
(3.056)
(4.279)
33.1%
66.9%
0.132*
0.087*
0.160*
(6.635)
(2.747)
(6.787)
30.4%
-0.001
-0.019
0.011
(0.608)
0.016
(0.523)
(-0.282)
-0.011
(-0.608)
0.046
81.9%
-0.021
-0.105
69.6%
0.004
18.1%
0.009
70.6%
29.4%
-1.008
-2.810
26.4%
73.6%
Equation 2: Explained variable: Probability
0.846*
0.778*
1.272*
(12.921)
(8.617)
(12.297)
-0.033*
-0.034*
-0.042*
0.246*
(15.296)
Marital status
-0.123
19.1%
-0.002
(-36.659)
Education
81.0%
92.7%
Total difference
Age
0.029
-1.596
-0.025
(0.618)
Constant
19.0%
(0.684)
0.004
0.013
0.375
80.0%
(2.673)
0.000
0.084*
(30.698)
20.0%
(2.275)
(0.055)
Sector
(2.229)
(4.005)
(2.124)
Length of service
0.090
0.180*
(-28.194)
(-26.730)
0.255*
0.232*
(10.498)
-0.005
(10.154)
0.682*
(5.942)
(-0.133)
(12.214)
-0.089*
-0.129*
-0.154*
(-9.362)
(-9.858)
(-7.603)
-0.268*
(-9.851)
Log likelihood
-8053.441
LR test of indep. eqns.
1057.800
(rho = 0): chi2(1) =
Prob > chi2 =
0.000
* Significant at the 1% level
-4356.007
-3315.474
671.010
0.030
0.000
0.855
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24
This table shows the estimations results for two regressions: the first one is the wage estimation and the second one the probability-of-participating-in-the-labor-market estimation. We
include in this table a statistic that is specific to Heckman's correction. The statistic “LR test
of indep. eqns” (“Likelihood ratio test of independent equations”) tests whether Heckman's
correction is necessary or not. The null hypothesis assumes that there is no link between the
probability equation and the wage equation; in that case, Heckman's method is pointless. The
null hypothesis is rejected when the statistic “chi2(1)” is large enough.
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Résumé
Etablir scientifiquement l’existence et l’importance d’une éventuelle discrimination salariale
selon le sexe se heurte à des difficultés conceptuelles et techniques dont la portée n’est pas
toujours reconnue : notre analyse d’un grand échantillon de données pour la Suisse en 1997
aboutit à la conclusion que – selon l’approche utilisée – il y a discrimination significative
contre les femmes ; ou que l'on ne peut détecter de discrimination ; ou qu’il y a discrimination
significative contre…les hommes. Les approches utilisées sont : la régression directe générale
(pour des qualifications et autres attributs donnés, les salaires sont-ils différents selon le
sexe?) ; la régression inverse générale (pour un salaire donné, les employeurs demandent-ils
des qualifications et autres attributs différents selon le sexe?) ; la méthode de Oaxaca-Blinder
(l’effet d’un attribut – l’âge ou l’état civil, par exemple – sur le salaire peut différer selon le
sexe et il faut donc estimer et comparer des équations séparées pour les femmes et pour les
hommes) ; la correction de Heckman (le fait de se concentrer sur les seules personnes employées peut engendrer un biais de sélection). Notre conclusion générale est agnostique: dans
l’état actuel des techniques et des connaissances, il n’est pas (encore?) possible de se prononcer scientifiquement sur l’existence ou non, en Suisse, d’une discrimination salariale fondée
sur le sexe. Cette conclusion se démarque donc de celle des études préexistantes, lesquelles
tendaient à établir l’existence d’une discrimination contre les femmes. L’absence d’une telle
discrimination ne veut cependant pas dire que les deux sexes ont les mêmes chances sur le
marché du travail et que tout est pour le mieux dans le meilleur des mondes non sexistes.
Abstract
Trying to ascertain scientifically the existence and importance of gender-based salary discrimination runs into conceptual and technical difficulties, the implications of which are not always fully appreciated: depending on the approach used, our analysis of a large sample for
Switzerland in 1997 concludes that there is significant discrimination against women; or that
no discrimination can be detected; or that there is significant discrimination against...men.
The approaches used are: direct general regression (for given attributes such as qualification
levels, do salaries differ according to gender?); inverse general regression (for a given salary
level, do employers require different attributes, such as qualification levels, depending on
gender?); the Oaxaca-Blinder method (the effect of a given attribute – e.g. age or marital status – on salaries may differ depending on gender and one must therefore estimate and compare separate equations for women and for men); Heckman’s correction (focusing on working
persons only may give rise to a selection bias). Our general conclusion is agnostic: given the
present state of techniques and knowledge, it is not (yet?) possible to ascertain scientifically
the existence of gender-based salary discrimination in Switzerland. This conclusion differs
from that reached by pre-existing studies, which tended to underpin the existence of salary
discrimination against women. The absence of wage discrimination however does not mean
that the two genders have the same chances in the labor market and that all is for the best in
the best of non-sexist worlds.
Zusammenfassung
(…)
Keywords: gender-based salary discrimination; direct and inverse regressions; the OaxacaBlinder approach; Heckman’s correction; Switzerland.
JEL Classification: J71; J31; D63; C29
25