European Journal of Population 4 (1988) 97-116
North-Holland
97
STATIC V E R S U S D Y N A M I C A N A L Y S I S OF T H E I N T E R A C T I O N
BETWEEN FEMALE LABOUR-FORCE PARTICIPATION
A N D FERTILITY
Erik KLIJZING *
University of Amsterdam, The Netherlands
Jacques S I E G E R S
University of Utrecht, The Netherlands
Netherlancls Interuniversity Demographic Institute, The Hague, The Netherlands
Nico KEILMAN
Netherlands Interuniversity Demographic Institute, The Hague, The Netherlands
Loek GROOT
University of Limburg, Maastrieht, The Netherlands
Received February 1988, final version received June 1988
Numerous studies have found a negative relationship between female
labour-force participation and fertility. In theory, there could be three explanations of
this finding: (i) causality runs from labour-force participation to fertility, (ii) causality
runs from fertility to labour-force participation, (iii) causality runs both ways. Alternatively, the relationship may not be a causal one. In practice, empirical studies covering
a wide range of Western countries at different times, and utilizing a great variety of
methods and techniques, have shown all four possibilities to be plausible. This may be
because outcomes differ from country to country for socio-cultural reasons, or from
period to period for historical ones. If so, applying various methodologies to data for
one country at a particular point in time should yield consistent results that all point in
one direction only. If they did not outcomes would appear to be method-dependent.
The single data set used in this study refers to the Netherlands in 1984 (ORIN project).
The relationship between fertility and labour-force participation in this data set is
investigated by means of three methodologies, ranging from 'static' to 'dynamic', i.e.,
Abstract.
* Author's address: Planning and Demography Department, University of Amsterdam,
Jodenbreestraat 23, 1011 NH Amsterdam, The Netherlands.
0168-6577/88/$3.50 © 1988, Elsevier Science Publishers, BN. {North-Holland)
98
E. Klijzing et at. / Female labour force participation and fertility
differing according to the degree in which they take the temporal aspects of the
decision-making process underlying this relationship into account: simultaneous logit
analysis, Granger analysis and Markov analysis. Each main approach is applied in two
different ways or on two different subgroups, for a total of six applications. In spite of
diverging operationalizations of the basic variables, it turns out that four of these six
analyses favour the inference that fertility decisions do have an impact on labour force
participation decisions but not the other way around, whereas the other two confirm
earlier findings (from data sets collected during the 1970s) that the relationship is
reciprocal. Substantively, this might indicate that the pattern of covariance is changing.
But 'static' simultaneous togit analysis is the only method to consistently point at this
causal unidirectionality, while outcomes from Granger and Markov analysis depend on
the modality applied. Methodologically, this means that the issue of method-dependency, at least in this area, remains largely unresolved.
Rdsumd.
L'analyse statique oppos~e ~ l'analyse dynamique de l'interaction entre la
participation au march$ du travail fdminin et la f~conditd
De nombreuses 6tudes ont montr6 une relation ntgative entre la participation au
march6 du travail ftminin et la f~conditt. ThEoriquement il peut y avoir trois explications possibles ~ c e r&ultat: (1) la participation au marchE du travail influe sur la
fdconditE, (2) la ftcondit6 influe sur la participation au marchE du travail, (3) i'influence peut ~tre rtciproque. I1 est m~me possible que la relation ne soit pas causale.
Pratiquement, les ~tudes empiriques qui couvrent un large 6ventail de pays dtveloppts
difftrentes @oques et qui utilisent une grande varitt~ de m&hodes et de techniques,
ont montrE que les quatre possibilitts pouvaient &re envisagtes. Cela peut &re d~ au
fait que les r&ultats different selon les pays pour des raisons socio-culturelles, ou selon
les ptriodes pour des raisons historiques. S'il en est ainsi, en appliquant difftrentes
approches ~ des donntes concernant un pays ~ un moment donnE, on devrait obtenir
des r&ultats compatibles qui conduiraient 5 la m~me explication. Cependant si ces
rtsultats ne sont pas compatibles, il en r&ulterait une dtpendance ~ la mtthode
utilis~e. Les donntes utilistes ici concernent les Pays-Bas en 1984 (Projet ORIN). La
relation entre fdcondit6 et participation au march6 du travail est analyste au moyen de
trois mtthodes difftrentes allant des 'm&hodes statiques' aux 'm&hodes dynamiques',
c'est-~-dire difftrant dans leur approche des aspects temporels du processus de d~cision
sous-jacent : analyse ~t l'aide d'un module logistique simultant, analyse de Granger et
analyse selon un processus de Markov. Chaque approche est utitiste de deux fa~ons
diffErentes ou sur deux sous-groupes diffErents, soit au total six applications. I1 en
rtsulte clue quatre de ces six analyses viennent appuyer l'hypoth&e que les dtcisions
touchant la ftcondit6 ont un effet sur les dtcisions touchant la participation au marchE
du travail, ta rdciproque n'~tant pas vtrifite, tandis que les deux autres viennent
confirmer des r&ultats anttrieurs (issus de donnEes portant sur 1970) montrant que la
relation est rtciproque. Cela peut indiquer un changement dans les relations. Mais
l'analyse 'statique' est la seule mEthode indiquant de fa~on consistante cette dEpendance locale, tandis que les deux autres analyses donnent des rtsuttats difftrents selon
la modalit6 appliquEe. MEthodologiquement, cela signifie que la dtpendance des
r&ultats aux mtthodes utilistes est encore un probltme non rtsolu, du moins dans le
domaine explore ici.
E. Ktijzing et at. / Female labour force participation and fertility
99
1. Introduction
Numerous studies have found a negative relationship between female
labour-force participation and fertility. In principle, there are three
possible explanations for this negative association:
(1) causality runs from labour force participation to fertility,
(2) causality runs from fertility to labour force participation,
(3) causality runs in both directions.
The first possibility implies that the woman decides to participate in
the labour market irrespective of her fertility intentions. Given her
labour-market participation, she is less likely to decide in favour of
having a baby than are women who are not employed. With the second
possibility, matters are reversed: any fertility decision is taken independently of attitudes towards labour-force participation. Given the time
spent on the bearing and rearing of children, she is less likely to enter
the labour market. The third possibility implies that each decision is
influenced by the other in some way. The fourth possibility applies
when any statistical correlation between the two variables vanishes
when extraneous factors are controlled.
Empirical studies covering a wide range of countries and periods,
and utilizing a great variety of methods and techniques, have demonstrated all four possibilities to be plausible. This may be because
outcomes differ from country to country for socio-cultural reasons, or
from period to period for historical reasons. If so, applying various
methodologies to data for one country and one period should yield
consistent results, all pointing to one possibility only as the most likely.
If they did not, outcomes would appear to be method-dependent. That
is the issue we shall be exploring in this paper, by approaching the
study of female labour-force participation and fertility from three
different methodological perspectives. Before turning to a discussion of
the methods and their results, we shall first highlight a few characteristics of the single data set used in this study.
2. The data
The data on which all three analyses are based come from a Dutch
survey conducted in 1984 among a representative sample of 1600
100
E. Klijzing et at. / Female tabour force participation and fertility
persons aged 18 to 54 years (ORIN 1). The principal aim of this project
was to investigate the dynamics of household formation and dissolution. Information on individual household status changes was collected
by means of a single-round retrospective interview. In order to minimize recall lapse, the reference period was restricted to the last seven
years prior to the interview, i.e., from January 1, 1977 to January 1,
1984. Besides changes in individual household positions, changes in
residence, labour-force participation and fertility were also recorded for
the same reference period. This makes possible an in-depth analysis of
the interaction between these various event histories. All events were
registered according to the calendar year and m o n t h of their occurrence. Here we will report on the interaction between female labourforce participation and fertility during the reference period.
3. Methods and results
As stated above, the relationship between female labour-force participation and fertility will be examined using three different methodologies. These are: (1) simultaneous logit analysis, (2) Granger analysis
and (3) Markov analysis. The first is based on two-stage m a x i m u m
likelihood logit analysis of a cross-section of O R I N data at the time of
the survey. This analysis may be said to be static in the sense that no
attention is paid to the time dimension implicit in any decision-making
process. Due consideration of the dynamic properties of this process is,
however, given in the third method mentioned which is based on a
particular approach stemming from mathematical statistics. The second
method developed in econometrics takes a more or less intermediate
position with respect to the static-dynamic continuum: time is heeded
but at an aggregate level. These three methods will now be briefly
introduced and their results discussed. Each main approach is applied
in two different ways or on two different subgroups so that there are
six different applications altogether.
1 The ORIN survey was carried out by the Netherlands Interuniversity Demographic Institute
(NIDI) in collaboration with the Universities of Amsterdam, Tilburg and Wageningen. The
research team consisted of D.J. van de Kaa, F.K.H. Klijzing, N.W. Keilman, H.G. Moors, A.C.
Kuijsten, L.Th. van Leeuwen, C.J. Weeda and P.A.M. van den Akker. The project was funded by
the National Programme of Demographic Research.
E. Klijzing et aL / Female tabour force participation and fertility
101
3.1. Simultaneous logit analysis
In order to disentangle the effects involved in mutual causation
between two or more variables through regression analysis, simultaneous estimation procedures are required (Bronfenbrenner (1953),
Koutsoyiannis (1973)). In the present case, this means that at least two
regression equations have to be estimated, one for female labour-force
participation and one for fertility. Both labour-force participation
(LFP) and fertility ( F ) have here been defined as dichotomous variables. That is, LFP = 1 if the w o m a n was gainfully employed at the time
of the interview, otherwise LFP = 0. Likewise, F = 1 if she h a d one or
m o r e children aged five years or less at h o m e at the time of the survey,
and F = 0 if not. As an appropriate approach in case of dichotomous
dependent variables, a logistic specification is used:
z = 1/(1 + exp(-f(x))),
with
z = dependent variable
x = (vector of) independent variable(s).
To allow for the possibility of simultaneity in the relationship between
labour-force participation and fertility, following Mallar (1977), a
two-stage m a x i m u m likelihood analysis was applied. For example, the
right-hand side of the equation explaining labour-force participation
contains the logit 2 of fertility. This logit is estimated from a reduced
form equation explaining fertility through all the exogenous variables
of the model except labour-force participation. The same procedure is
followed for the calculation of the logit of labour-force participation.
The exogenous variables in the model are the w o m a n ' s age, her
educational attainment, marital status and, if in a marital or cohabitational union, its duration and her partner's income as well. For clarity's
sake, table 1 presents only the effect coefficients pertaining to fertility
and labour force participation with respect to each other 3; on the
left-hand side for all w o m e n concerned ( N = 840) and on the right-hand
for married w o m e n only ( N = 229). Each equation was solved for six
different definitions of 'work': 1, 8, 16, 24, 32 and 40 hours or more per
2 L o g i t v = ln{ v/(1 - v)).
3 I n f o r m a t i o n o n the o t h e r c o e f f i c i e n t s c a n b e o b t a i n e d f r o m the a u t h o r s o n request.
E. Klijzing et aL / Female labour force participation and fertility
102
Table 1
Regression coefficients a of simultaneous logit analysis measuring the effects of labour force
participation (LFP) on fertility ( F ) and vice versa, for all women and married women only,
according to the number of hours worked per week. O R I N , 1984.
Explanatory
variable
LFP
Number
of weekly
hours
worked
> 1
F
LFP
> 8
F
LFP
>_ 16
Dependent variable
All women
Married women o n l y
LFP
F
LFP
F
×
- 0 . 3 3 4 (2.03)
0 . 0 7 4 (0.03)
×
×
- 0 . 5 8 7 (2.60)
- 0 . 5 7 7 (0.32)
×
x
- 0 . 1 8 0 (1.07)
- 0 . 1 8 0 (0.03)
X
x
- 0.545 (2.38)
- 0 . 3 0 4 (0.29)
×
0 . 0 6 6 (0.03)
×
- 0 . 5 6 1 (2.25)
- 0 . 4 3 4 (0.32)
×
×
F
LFP
_> 24
> 32
> 40
0.054 (0.03)
0.155 (0.77)
×
×
- 0 . 3 4 3 (1.31)
- 0 . 7 0 5 (0.38)
×
0.171 (0.70)
- 0 . 0 3 4 (0.04)
X
×
- 0 . 4 1 6 (1.36)
- 0 . 2 4 0 (0.38)
×
0 . 0 1 9 (0.06)
- 0.026 (0.04)
×
×
- 0 . 5 1 8 (1.32)
- 0.178 (0.38)
x
×
F
LFP
×
×
F
LIP
0.051 (0.27)
x
F
a Figures between parentheses indicate t-value (without sign) corresponding to effect coefficient.
week. Previous research has demonstrated that it may make a difference which lower limit is selected (Siegers (1985)).
The results in table 1 confirm that the relationship between female
labour-force participation and fertility is indeed mostly negative, although statistical significance only applies to the effects of fertility on
labour-force participation at LFP > 1 hour for all women, and at
LFP >_ 1, 8 and 16 hours for married women. There is no statistical
evidence for the existence of mutual causality: nowhere is the effect from
labour-force participation on fertility found significant. This leaves us
with possibility number (2) (see Introduction) as the most plausible.
3.2. Granger analysis
Granger analysis is basically time-series analysis: the interaction
between two or more variables is investigated by comparing their data
over time. Its concern with time clearly distinguishes Granger analysis
from simultaneous logit analysis as performed in the previous section.
The postulates behind Granger analysis are the following: (1) the time
E. Klijzing et al. / Female labourforce participation and fertility
103
series are to be seen as representing stochastic, not deterministic,
processes; (2) they are stationary, i.e., both mean and variance are
independent of the time index 4, and (3) the future has no influence
whatsoever on either past or present. We will not elaborate on these
premises here, since this has already been done elsewhere (see, for
instance, Pierce and Haugh (1977)). As we shall see, the third postulate
is of particular interest to our application.
Granger causality is usually defined in terms of the reduction in the
error of prediction. That is, suppose f2t represents all (relevant) information available at time t, and that predictions are wanted for xt+l,
one on the basis of I2, including present and past values of y and
another one on the basis of f2t excluding past and present values of y
(i.e., Yt-j, J >-0). If the former prediction performs better than the
latter, then, apparently, y carries special information with respect to x
and so the inference is made that causality runs from Yt-j to xz+ ~ ( j ,
k >__0). In practice, the decision as to which equation predicts better is
taken on the basis of the reduction in the error of prediction, o 2. We
can now rewrite the four alternatives of causation at the beginning as
follows:
(1) y ~ x (meaning y causing x) i f ° 2 ( X t + l I x t - j , Y t - j ) ~"
o2(2,+1 I x,_j); similarly,
(2) x ---,y i f 02(-gt+ltYt_j, x t _ j ) < 02(-9t+1 I.Ft--l);
(3) x m y if both conditions (1) and (2) apply (feedback);
(4) x and y are independent if 0 2 (2,+ 1 I x,_j, Yt-j) = o2(2,+l t x,_j)
and if a 2 (_9,+1 l Y,-j, x,_j) = 0 2 ( - 9 t + 1 }y,_i).
In the literature on Granger causality, four different methods are
usually distinguished: the H a u g h - P i e r c e approach, the 'direct' Granger
approach, Sims' approach and the five-steps approach advocated by
Ashley et al. (1980). Here we will - for reasons of parsimony concentrate on the second and third approaches only, where Sims'
appIication can be seen as a form of 'indirect' Granger analysis.
In the bivariate case, direct Granger analysis consists of the regression of x, on the past values of x, and Yt- If the coefficients corresponding to the lagged values of Yt differ significantly from zero, it is
said that y 'Granger-causes' x. If, on the other hand, in a regression of
y on x the coefficients corresponding to the lagged values of x t differ
4 In other words, E(xt) = E(x,+k) and o2(xL) =
o2(xr+k),
104
E. Klijzing et at. / Female labour force participation and fertility
significantly from zero, then x 'Granger-causes' y. If both tests yield
positive results, causality runs both ways.
In Sims' version of Granger analysis, x, is regressed not only on the
past values of x and y but on the future values of y as well. Future
here refers, of course, to some time beyond t, for which measurements
on y are still available. With respect to this relative future concept,
Sims (1972, p. 541) has said: 'If and o n l y if causality runs one way
from current and past values of some list of exogenous variables to a
given endogenous variable, then in a regression of the endogenous
variable on past, current and future values of the exogenous variables,
the future values of the exogenous variables should have zero coefficients'. If they do not, this is interpreted as indicating, not that Y,+I
determines x t (because this would be contrary to the third postulate of
Granger analysis), but that x, determines y,+ 1.
The two time series, L F P and F were constructed in the following
way. For each month in the seven-year period 1977-1984, the percentage of women who participated on the labour market for 1, 8, 16,
24, 32 or 40 hours or more per week was computed. (In actual fact, it
was not these percentages themselves that were recorded but their
aggregate change from month to month.) The fertility for all sample
women was measured as the number of children born per month. This
time series was then shifted ten months backwards so as to estimate the
probable m o m e n t of the fertility decision. 5 This has resulted in two
time series of 74 observations each. Because both time series represent
first differences, the stationary condition is satisfied. In order not to
clutter the output too much, lags ( - ) and leads ( + ) of the independent
variable were varied from one to four months only. The following four
regression equations have been estimated for each work definition (1, 8,
16, 24, 32, 40 or more hours per week):
Direct analysis (Granger)
Indirect analysis (Sims)
F= f(LFP: 4 lags+present)
L F P = f ( F : 4 lags + present)
F = f ( L F P : 4 lags + 4 l e a d s + p r e s e n t )
LFP = f ( F : 4 lags + 4 leads + present)
Values of the regression coefficients corresponding to direct Granger
analysis are presented in table 2 and those to indirect Granger analysis
5 This assumes that every birth is the outcome of a conscious decision process preceding
conception. This will certainly not always be the case. The assumption that a status change is
always wanted is particularly strong if applied to withdrawals from the labour market.
E. Ktijzing et al. / Female labour force participation and fertility
105
Table 2
Regression coefficients of direct G r a n g e r analysis m e a s u r i n g the effects of l a b o u r force participation o n fertility (upper panel) and vice versa (lower panel) for various m i n i m a l n u m b e r s of w e e k l y
hours worked. O R I N , 1 9 8 4 .
Lags/
leads
Minimal
n u m b e r of hours w o r k e d per w e e k
L F P >_1
L F P >_8
LFP > 16
L F P >_2 4
L F P >_3 2
LFP >
-1.003
-0.923
40
Fertility regressed on labour force participation
+4
+3
+2
+1
0
-0.537
-0.645
-1.110
-1.179
-0.890
-0.999
-0.806
-0.153
-0.053
-0.104
- 1.419 ~
- 1.528 a
- 1.886 "
- 1.757 a
- 1.580 a
- 1.436 a
- 3
- 2.330 ~
- 1.991 a
- 2.195 a
- 1.767
--
-
- 0.764
- 0.824
- 0.672
- 1.104
-1
--
2
4
FGranger
6.62 a
6.98 a
9.72 a
a
a
1.995 a
- 0.866
11.77 a
16.61 ~
-
1.842 a
- 0.722
17.19 a
Labour force participation regressed on fertility
+4
+3
+2
+1
0
- 1
- 2
- 3
- 4
FGranger
Significant
0.030
0.015
- 0.007
- 0.015
- 0.030
- 0.026
~- 0.020
- 0.005
0.011
- 0.003
- 0.013
- 0.010
0.006
- 0.004
- 0.014
0.009
- 0.006
- 0.020
- 0.047
- 0.048
- 0.041
- 0.056
- 0.045
- 0.052
- 0.050 a
- 0.043
- 0.041
- 0.047
- 0.046
- 0.045
4.16 a
4.29 a
5.23 "
5.97 a
a
7.77 a
8.55 a
at p < 0.05.
in table 3. In both tables, values of the F-statistic indicating overall
significance of the regression equations are given as well. To start with
table 2, it can be seen that the relationship between female labour-force
participation and fertility is again mostly negative. Interestingly, the
effects of labour-force participation change on parity progression ratios
(table 2, upper panel) are strongest if observed moments of labour-force
participation change are lagged two to three months relative to observed moments of fertility status change, for all values of minimum
working hours. No such regularity exists in the regression of labour
force participation on lagged fertility changes. According to the corresponding F-statistics, however, overall significance is achieved for both
E. Klijzing et al. / Female labour force participation and.fertility
106
Table 3
Regression coefficients of indirect Granger analysis measuring the effects of labour force
participation on fertility (upper p a n e l ) a n d v i c e versa (lower panel), for various minimal numbers
of weekly hours worked. O R I N , 1 9 8 4 .
Lags/
Minimal number of hours worked per week
leads
LFP > 1
L F P >_ 8
L F P >_1 6
LFP > 24
L F P >_ 3 2
L F P >_ 4 0
-0.792
-0.824
a
-1.418
a
Fertility regressed on labour force participation
+4
- 1.394 a
-1.417
a
-1.295
a
-0.972
+3
-1.573
-1.814
a
-1.447
a
-1.449
+ 2
- 0.223
- 0.269
+1
a
- 0.464
--0.306
0.110
-0.485
0
0.262
0.218
- 0.341
- 1
- 0.227
-2
-1.304
--3
--1.862 a
--4
--0.027
Fsims
- 0.270
a
3.14 a
-1.523
- 0.220
- 0.036
a
--1.615 a
-1.571
a
a
- 0.216
- 0.234
0.008
0.045
0.121
- 0.386
- 0.334
- 0.271
0.136
a
-1.438
-1.619
0.632
a
0.511
-1.501
-1.329
a
--1.992 a
--1.603 a
--1.842 a
--1.806 a
0.026
--0.205
--0.415
--0.376
--0.238
3.05 a
2.51
3.80 a
4.10 a
4.82 a
Labour force participation regressed on fertility
+ 4
- 0.024
- 0.032
- 0.018
- 0.032
- 0.026
+ 3
0.018
0.015
0.024
0.011
0.001
- 0.029
0.008
+ 2
- 0.054 a
- 0.035
- 0.038
- 0.045
- 0.060 a
- 0.065 a
+1
-0.009
-0.017
-0.029
-0.044
-0.053
-0.052
0
0.002
0.002
0.014
0.032
0.052
0.040
- 1
0.041
0.025
- 0.003
- 0.007
- 0.022
- 0.016
-
2
- 0.006
0.010
0.022
0.018
0.012
0.015
- 3
0.016
0.006
- 0.009
0.020
0.006
- 0.005
- 4
- 0.029
- 0.032
- 0.027
- 0.037
- 0.023
- 0.027
0.81
0.63
0.79
1.21
1.71
1.58
Fsims
a Significant at p ~ 0.05,
directions of causation, which would thus seem to favour the hypothesis of mutual influence as the most adequate. But this finding is not
supported by the results of Sims' indirect Granger analysis in table 3.
In the upper panel of table 3, fertility is regressed on labour-force
participation as an explanatory variable shifted zero to four months
backward ( - ) or forward ( + ) with respect to the moment of fertility
decision. If backward, at - 2 to - 3 months, more or less the same beta
coefficients hold as those in table 2, in spite of the fact that the fertility
equation has now been expanded with four additional explanatory
variables. If forward, the corresponding regression coefficients should
not deviate significantly from zero, because chronologically speaking
E, Klijzing et at. / Female labour force participation and fertility
107
the future has no bearing on either past or present. If they do deviate
significantly from zero, then this indicates that causation runs from
dependent to explanatory variable. As the corresponding F-statistics
indicate, in five out of six cases these effects were found significant.
The only time that this does not hold true - namely, when labour-force
participation is defined as working at least 16 hours a week - the value
for the F-statistic (2.51) comes very close to the critical m i n i m u m of
2.53. Therefore, it may be safely concluded that fertility decisions do
have an impact on 'future' labour-force participation. This is particularly true at leads of three to four months.
But not so the other way around, as the results in the lower panel of
table 3 indicate. Here, labour-force participation is regressed on fertility. Regression coefficients representing the effects of 'future' fertility
on present participation do not differ significantly from zero (except
for the three of the six which correspond to a shift of two months), so
there are hardly any grounds for inferring a definite influence from the
latter on the former. No matter which work definition is used, the
overall F-statistic never comes anywhere near the critical minimal
value of 2.37 necessary for rejecting the null hypothesis. The only
conclusion warranted, therefore, is that labour-force participation has no
influence on subsequent fertility decision-making. Whereas direct Granger
analysis favoured the third possibility of causation, results from indirect Granger analysis rather point to the second possibility we identified. 6
3.3. Markov analysis
The third research strategy to be followed is one inspired by a
biomedical study of the possible effects of menopause on the outbreak
of a particular skin disease, pustulosis palmoplantaris (AMen et al.
(1980)). That study demonstrated how a simple, time-continuous
Markov model can be used to analyze the interaction between two life
history events, where the occurrence of one may change the intensity at
which the other takes place. Courgeau and Lelitvre (1988) have applied
6 We are indebted to one of the referees for pointing out the close parallel, both in contents and
reach, between our Granger analysis and the one published by Robert Michael, 'Consequences of
the rise in female labour-participation rates: questions and probes', Journal of Labour Economics,
Vol. 3 (1985) no. 1, pp. 117-146 (in particular, pp. 138-145).
E. Kl~zing et al. / Female labour force participation and fertility
108
I
~
(la)
P*=e
X
\
v P~e
\ \ \P~b\i
Pb~
\
N
B,N
E=411
B= 25
]
18.531
I.
5
4
9
v~
(Ib)
2
6
3
2
-83.392
N= 91
B=2b,N=15[
N=276
B= 87
[[
- 7 . 6086
9
v~
(Ic)
4
2
8
44.851
E= 47
B=0,E=9 I
Fig. 1. The Markov model.
a similar model in their study of the interaction between getting
married and the abandoning of an agricultural occupation.
Let B in fig. l a stand for any parity progression (without number
specification), whereas N represents the transition from E (employed)
to not employed, together with the corresponding transition probabilities Pbe, Pbn, Pne, and Pnb- In the present analysis, fertility remains
E. Klijzing et al. / Female labour force participation and fertility
109
unspecified as to parity. This simply means that all women qualify for
entering the chain reaction from the time of their getting (re)employed,
irrespective of their number of offspring. Those who reach the final
state in fig. l a have, in the end, one child more than at the beginning.
Labour-force participation was operationalized as a dichotomous variable distinguishing between employed and not employed. The former
state is independent of the actual number of hours worked per week.
This implies that, in the present application, transitions from full-time
to part-time work or vice versa are treated as censored observations.
Each time that such a transition occurs, the counting process is started
afresh. This relative insensitivity may be improved u p o n in later
versions of the model, for instance by considering full-time and parttime employed as separate states. Fertility will then be specified by
parity as well.
Because the status 'employed' provided the largest number of observations to start with, we shall concentrate our discussion on fig. lb.
(Fig. lc pictures the flow of events if ' n o t employed' is selected as the
point of departure.) The figures in fig. l b are to be read as follows:
411
25
15
91
26
women start employment at time t;
of them then have a baby, after which
withdraw;
of the entrants leave the labour force again after some time;
of them have a baby subsequently.
Thus, starting from the upper-left corner, women having entered the
labour market are, irrespective of their number of offspring at that
time, exposed to three competing risks. They may either first experience a parity progression or a withdrawal from the labour market, after
which they may re-enter at E once they get employed again. Thus,
multiple labour-force entries are duly accounted for in this model,
which operates as a simple increment-decrement life table. A third
possibility consists of both events occurring simultaneously, in which
case a diagonal course is followed (fig. la).
In fact, three different types of ties may present themselves:
E ~ B,
BuN
and
E ~ N.
In all three cases it is factually impossible to put events in sequential
order. Whether two or more events are to be considered as simulta-
E. Klijzing et aL / Female labour force participation and fertility
110
Table 4
Ascertaining the effects of ties on the magnitude of transition probabilities. OR/N, 1984.
Sequence
Ties not
modelled
Tie widths (months)
1
3
6
9
Relative number of ties (%)
E~ B
0.0
0.0
0.2
0.9
2.1
11.0
11.0
11.9
12.2
12.5
0.1
0.1
1,0
2.6
5.7
(E ~ ) N -o B 1
(E~)B~N]
E~ N
l
Two-year transition probabilities (%)
E -~ B
(E -* ) N -* B
6.3
23.3
5.5
23.2
5.3
23.7
5.I
22.1
5.0
24.1
(E -~ ) B -~ N
E -~ N
35.3
13.6
35.3
12.8
32.9
12.6
29.7
11.6
30.4
10.5
T-statistic measuring significance of difference between pairs of transition intensities ~
E~B~
(E ~ ) N ~ B J
- 3.178
- 3.311
- 3.401
- 3.264
- 3.495
(E ~ ) B - ~ N ~
E-~ N )
1.750
1.806
1.700
1.604
1.730
a See footnote 7 below.
neous, depends on the 'fuzziness' of the time unit chosen. The larger
this unit, the greater the number of occurrences of simultaneity, as is
demonstrated in the upper part of table 4 (for tie widths of 1, 3, 6 and 9
months, respectively). Excluding them will generally tend to deflate the
corresponding transition probabilities, as can be seen from the middle
part of table 4. This is so because of the selection for longer 'survival'
times. But since the relationships between the relevant pairs of transition rates remain largely intact, we might as well leave the issue of
simultaneity at rest. v In the remaining section, all results to be pre7 The insensitivity of the relationship between the relevant pairs of transition rates to the
inclusion or exclusion of ties is illustrated by the fact that the values of the T-statistic according to
tie width in the lower part of table 4 remain virtually unchanged. (The T-statistic tests for the
difference between two transition intensities and has an asymptotic, normal distribution, with
mean 0 and asymptotic variance 1 (Hoem and Funck Jensen (1982)).) Time-constant intensities
are assumed to apply in this time-continuous Markov model.
E, Klijzing et al, / Female labour force participation and fertility
11t
sented are based on the inclusion of ties, as it was easier to include
them.
The two horizontal lines in fig. l a represent the occurrence of a live
birth, the upper one from condition E and the lower one from
condition N, given E. If the probability Pbe 4=Pbn according to some
suitable test statistic, it is likely that the two subgroups come from
different 'survival' distributions. If so, the inference is made that
labour force participation status affects the chance of having a baby.
The two vertical lines represent the transition from employed to not
employed, on the left-hand side from any parity, and on the right-hand
side from one that is one rank higher. If Pne differs significantly from
Pnb, an influence from fertility on the chance of leaving the labour
market is assumed. If both the 'horizontal' and 'vertical' test returns
are positive, reciprocal influence is concluded. If one of them turns out
to be negative, local dependence (in one direction only) is indicated. If
both tests fail, the relationship is said to be spurious.
The test statistic used in this paper to distinguish between these
various alternatives is the Lee-Desu (1972) statistic summarizing the
relative difference in waiting time positions between sample groups.
For each individual a U score is computed by comparing the individual's exact survival time (in months) with those of all other sample
members. This score, initially set to zero, in increased by one for each
case whose survival time is found to be less than the individual's, and
decreased by one for each case whose survival time is found to surpass
the individual's. If two members survive the same length of time but
one is censored and the other is not, the censored observation is
considered to have the longer survival time. The U score for a censored
observation is simply the number of uncensored observations with
survival times less than that of the censored observation. No cases can
be known to have survival times greater than that of the censored
observation. Where it cannot be determined who survived longer (due
to ties or both observations being censored), there is no change in
score.
The U scores for all members of the same subgroup are then added
so as to express their 'joint' survival time rank order position relative to
that of other subgroups. If one subgroup is predominantly made up of
'short interval' members, its U total may be negative. If long intervals
prevail, the total score wilt be high and positive. For instance, 2 U
corresponding to Pbe in fig. lb amounts to 18.5 as compared to - 8 3 , 4
E. Klijzing et al, / Female labour force participation and fertility
I12
Table 5
Values of the L e e - D e s u statistic indicating the relative difference in average decision time in
f a v o u r of withdrawal from the labour market (L, upper pmael) vis-a-vis fertility ( F , l o w e r panel),
as estimated by differentially lagging observed moments of transition events (3, 6, 9, 12 a n d 15
months): employed women. O R I N , 1984.
~0
~3
~6
~9
~12
~15
97,357
94.965
24.209
27.561
0,695 a
0.820 a
63.510
82.194
67.530
14.208
21.170
1.210 a
46,750
63.524
73.868
66.847
11.850
14.600
0.446 a
10.812
66.869
52.828
93.039
61.426
1.937 a
0.989 a
11.003
64.424
54.197
69.780
2.012 a
1.121 a
0.285 a
10.058
57.345
27.081
~rticaltest: ~ e e f f e c t ~ F o n L ~c#ions
L-O
L-3
L-6
L-9
L-12
L-15
35.749
0.040
0,012
0.004
0.023
0.017
a
a
a
a
a
28.935
35.112
0.142
0.154
0,052
0.202
~
a
a
a
92.202
28.054
30.214
0.469 a
0.412 a
0.473 a
Horizontal test: the effect of L on F decisions
L-0
L-3
L-6
L-9
L-12
L-15
77.402
131.369
124.263
105.619
85.249
56.951
75.518
76.635
126.110
109.769
85.696
57.450
14.025
73.885
66.980
112.451
88.361
56.485
a N o n - s i g n i f i c a n c e at the 0.05 level.
for Pbn, indicating that, on the whole, women take much longer to have
a baby when employed than when not. With 411 sample members
starting from E, the theoretical range for individual U scores is
0 _+ 410.
Based on these group-specific XU scores, a D-statistic 8 is then
computed which is asymptotically distributed as chi-square with degrees of freedom equal to the number of subgroups minus one, under
the null hypothesis that they all come from the same survival distribution. The larger the D-statistic, the more likely it is that the subgroups
come from different survival distributions in the population.
If we consider the first cell in the upper panel of table 5 (L-0, F-0),
where the influence of fertility on labour-force participation is at stake,
we see that D with 35.7 is significant at the five per cent level. Hence
the conclusion is drawn that, as far as the transition from employed to
s Let IVy = ~.Ui where the sum is over all cases in group j, then D = [ ( N - 1 ) B ] / T , w i t h N equal
to the sum of all cases, and B = X { W j 2 / N j } where summation is over all subgroups j, and
T = XU/2, for all cases i (1,2,3 . . . . . N ) .
E. Klijzing et al. / Female labour force participation and fertility
113
not employed is concerned, reproductive behaviour does make a difference. But the reverse holds true too. At D = 77.4 (table 5, lower
panel, first cell), the effect of labour-force participation status on the
chances of having a baby is found to be equally important, if not more
so. The combination of these two findings thus leads to the provisional
conclusion that the two variables are interactive.
But events as observed stand for status changes corresponding to
overt behaviour. What about the covert behaviour of the underlying
decision process that supposedly precedes these instantaneous transitions from one state to the other? Would it be possible to model this
sequential decision process in the same way as the event history
analysis just performed? One way of accomplishing this would be to lag
the observed moments of events by some reasonable amount of time so
as to approach the assumed moments of decisions. For fertility it is
obvious that the conscious decision to have a child is taken at least nine
months prior to delivery. Allowing for some three months conception
delay, it appears that twelve months represents a reasonable time lag.
Matters are somewhat less straightforward with decisions to give up
work. Most employers would request resignation letters at an average
of at least two months notice, depending perhaps on the length of
service. Or the decision may be forced on the individual, in which case
it is hard to speak of a freely chosen course of action on his or her side.
But suppose that the decision to quit were taken three months prior to
the factual departure.
The effects of these two particular time lags on the flow of 'events'
(derisions) can be ascertained by comparing the values of the D-statistic in the corresponding cells (F-12, L-3) of table 5. With D--82.2,
deciding to have a child still influences decisions to quit work, but the
reverse no longer holds true. Apparently, decisions to have a baby are
taken independently of labour-force participation decisions. This result is
also obtained for other time lags, as shown by the other a-marked
figures in the lower part of table 5.
To sum up, time lags L-3 and F-12 may appear reasonable on
logical grounds. But one of the two local dependencies observed
between factual status changes then gets dissolved. Labour-force participation at this level still remains a function of fertility, but children
are wanted for their own sake, whatever the woman's labour-force
participation intentions. This same result was obtained with 'not employed' as the model's source value, although the pattern of insignifi-
114
E. Klijzing et al. / Female labour force participation and fertility
cant values for the Lee-Desu statistic in that case is somewhat less
regular (figures not shown).
4. Discussion and final remarks
This paper has described three entirely different approaches to the
analysis of the interaction between two or more behavioural variables.
We applied the three methods, each in two modalities, to the interaction between female labour-force participation and childbearing, for a
total of six analyses. Before discussing substantive findings, we would
like to stress once more that there are important methodological
differences between the three main approaches. Firstly, the simultaneous logit analysis and the Granger analysis are both based on
regression methods, whereas the Markov model is an application of
survival analysis. Furthermore, of the two regression techniques,
Granger analysis works with untransformed variables (at least in this
case), while simultaneous logit analysis employs a logit transformation.
Secondly, the latter only considers states that women occupy (employed or not; one or more children under five years of age at home or
not) at one particular point in time. In the Granger study, on the other
hand, aggregate changes in labour-force participation over a seven-year
period are investigated, in conjunction with those in fertility. The
Markov model is the only one to treat explicitly the timing of individual
labour-market and fertility events. Thirdly, both Granger and Markov
analysis apply time lags in their relevant variables, but for different
reasons. In the latter approach this is done in order to shift the
emphasis from the level of events to the underlying level of decision
processes. The introduction of time lags and leads in Granger analysis,
on the other hand, is closely linked to the concept of Granger causality,
as strictly running from the past through the present to the future.
In spite of these and other differences, the findings reported in this
paper unanimously indicate a strong influence of fertility on labour
force participation, and - at least in one modality of each main
approach - a very weak if not negligible influence in the reverse
direction. Previous studies for the Netherlands, carried out on data for
the 1970s, revealed strong mutual influences (Siegers (1985)). This
finding is partly supported by the present analysis too. It would be
rather premature, therefore, to conclude, on the basis of the 1984
E. Kiijzing et at. / Female labour force participation and fertility
115
ORIN data alone, that two-way causation has now been totally disrupted. But perhaps Dutch women in the 1980s do somehow cope
better with the dilemma of how to combine motherhood and economic
activity than did women in the 1970s, in spite of government policies
having remained virtually unchanged over the last two decades. Perhaps this capacity is a sign of emancipatory forces gaining momentum
in the society at large, the general lack of political support notwithstanding. All that in the end then remains from the original (mutual)
relationship, is the purely biological constraint that if in labour, women
cannot be active in the labour market at the same time. Analyses of US
data for the period 1968-1973 that closely resemble our Markov
strategy also suggest a much stronger impact of fertility on female
labour-force participation than the other way around (Felmlee (1986)).
But, the main emphasis in this paper has been on methodological
issues rather than on substantive findings. As far as the direction of
causality between female labour-force participation and fertility is
concerned, 'dynamic' approaches like Markov and Granger analysis
lead to very much the same conclusions as 'static' approaches (like
simultaneous logit analysis). This does not necessarily mean that using
these 'static' methods will always be the best research strategy. There
are insights beyond the direction of causality that 'static' techniques do
not provide. Because of their representation of the processual aspects
of female labour-force participation and fertility behaviour, 'dynamic'
models are better equipped to explain why causality runs the way it
does. However, demonstrating this potential, in the context of life
course or event history analysis for instance, is beyond the scope of this
paper.
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