Fertility and female employment reconsidered:

A macro-level time series analysis�

Henriette Engelhardt, Tomas K�ogel and Alexia Prskawetz

Max Planck Institute for Demographic Research,

Doberaner Str. 114, D-18057 Rostock, Germany

January 31, 2001

Abstract

Our paper examines causality and parameter instability in the long

run relation between fertility and female employment. This is done by

cross-national comparison of macro-level time series data. By apply-

ing error correction models { a combination of Granger-causality tests

with recent econometric time series techniques { we �nd causality in

both directions. This �nding is consistent with simultaneous move-

ments of both variables brought about by common exogenous factors

such as social norms, institutions and �nancial incentives. We �nd

a signi�cant negative correlation until the 1970s, respectively 1980s

(depending on the country under investigation) and an insigni�cant

or weaker correlation afterwards. This result is consistent with recent

�ndings in the demographic literature which argue that changes in the

institutional context like childcare availability and attitudes towards

working mothers might have reduced the incompatibility between chil-

drearing and female employment.

�For helpful comments and suggestions we would like to thank Juha Alho, Tom DiPrete,

Ulf Christian Ewert, Tomas Frejka, Jan Hoem, Johannes Huinink, Michaela Kreyenfeld,

Thomas Lindh, Warren Sanderson and participants of the workshop on Demographic-

Macroeconomic Modelling in Rostock. The views expressed in this paper are the authors'

own views and do not necessarily represent those of the Max Planck Institute for Demo-

graphic Research.

1

1 Introduction

The relationship between fertility and female labor force participation is a

long-standing question in demography. A negative association between these

two variables is mainly argued for as evidence for the incompatibility of

raising children and staying in the workforce in today's society where the

place of work and home are mostly spatially separated. Therefore, decreasing

fertility is associated with increasing female employment and rising female

employment is associated with falling fertility. Up to now, it is unclear

whether these mutual relations are causal in one or the other direction.

The question \What causes what?" received renewed attention in the

demographic literature during the last years. This renewed interest resulted

from recent studies which have shown that a simple cross-country correlation

coe�cient between the total fertility rate and the female labor force partic-

ipation turned from a negative value before the 1980s to a positive value

thereafter. The question then arises whether there is a causal relationship at

all.

Several studies go beyond measures of correlation and explicitly test for

the existence and direction of causality between fertility and female employ-

ment. Due to substantive and methodological shortcomings these studies

have found con icting results. Our paper aims to clarify the literature by

taking into account parameter instability in the relation between fertility

and female employment and by applying recent econometric time series tech-

niques (so-called error correction models), which have not yet been applied

in an appropriate way to the fertility/female employment nexus.

Our results are twofold: (i) We �nd causality between fertility and female

employment in both directions. We argue that this is consistent with the view

that comovements of fertility and female employment are caused by common

exogenous factors. These factors can be social norms and social institutions

(factors that are stressed by sociologists and demographers), but also oppor-

tunity costs of childrearing and family income (factors that are stressed by

economists). (ii) Our empirical results show a signi�cant negative correlation

between fertility and female employment from the 1960s to the beginning of

the 1970s for all countries of our study. However, for the non-Mediterranean

countries in our sample the correlation becomes weaker (though still signi�-

cant negative) at the end of the 1970s and for some countries the correlation

becomes even insigni�cant. Therefore, our results are supportive for recent

�ndings in the demographic literature which convincingly argue that societal

2

level responses have eased the incompatibility between childrearing and fe-

male employment in most developed countries (Brewster and Rindfuss, 2000,

Rindfuss et al., 2000, and Rindfuss and Brewster, 1996). For the Mediter-

ranean country in our sample { Italy { we �nd the opposite result, that is, the

negative correlation between fertility and female employment becomes even

stronger across time. This �nding coincides with the argument in Rindfuss

et al. and Brewster and Rindfuss that we are only likely to see increasing

female employment no longer to depress fertility in those countries that suc-

ceeded in minimizing the incompatibility between childrearing and female

work. In Mediterranean countries this incompatibility between female em-

ployment and childrearing still persists.

The set up of our paper is as follows. In section 2 we �rstly discuss the

possible relationships between fertility and female labor force participation

from a micro theoretical point of view. Secondly, we discuss the gap in the

existing macro-level time series literature that we aim to close with our paper.

In section 3 we describe the data and in section 4 we explain the econometric

methodology that is applied in the paper. We present the results in section

5 and conclude in section 6.

2 Theoretical and methodological considera-

tions

2.1 Micro explanations

At the individual level, numerous studies have shown a negative associa-

tion between fertility and female labor force participation (e.g., Lehrer and

Nerlove 1986; Brewster and Rindfuss 2000). On average, women in gainful

employment tend to have fewer children, and women with children spend

less time in the labor market. Weller (1977: 43) lists four possible expla-

nations for this negative association between fertility and female labor force

participation:

1. women's fertility a�ect their labor force participation;

2. women's labor force participation a�ect their fertility;

3. both women's fertility and their labor force participation a�ect each

other; and

3

4. the observed negative relationship is spurious and is caused by common

antecendents of both variables.

According to the mentioned role incompatibility hypothesis both women's

fertility and their labor force participation a�ect each other reciprocally be-

cause of the strain between mother and worker roles. Nothing in this hy-

pothesis suggests causality in one direction rather than the other (Lehrer

and Nerlove 1986).

From the point of view of economic theory fertility and female employ-

ment are simultaneously determined by the same basic economic variables.

More speci�cally, female labor market participation and fertility are both

choice variables which households choose simultaneously given their exoge-

nous constraints. If both variables uctuate to some extent synchronously,

then { according to the logic of economic theory { this must be caused entirely

by external variables which determine both variables exogenously. Examples

of such external variables are the real female wage, the unemployment rate

and { recently accepted in some work by economists { social norms.

Many researchers would not go as far as economic theory and would argue

that at least part of the correlation between fertility and female employment

is not determined by external variables. Some of these researchers view

fertility and female employment more as the result of a sequential decision

process rather than the result of a simultaneous decision problem. If these

variables are indeed the result of a sequential decision process, then it is quite

possible that one variable exogenously causes the other variable.

2.2 Macro studies

Given the discussed explanations of the fertility/employment nexus on the

micro level, it is no wonder that previous empirical research has mainly con-

centrated on micro-level data (for an extensive review of the micro literature

see Cramer 1980; Lehrer and Nerlove 1986; Spitze 1988). Nevertheless, with

existing cross-sectional as well as longitudinal survey data it is very di�-

cult to resolve the fertility/employment question since the empirical �ndings

depend on the underlying decision model (sequential or simultaneous), and

therefore on the applied statistical model. Furthermore, work intentions may

cause actual fertility behavior and fertility intentions may cause actual work

behavior, i.e., future events may cause present behavior (Bernhardt 1993; N�i

4

Bhrolch�ain 1993). Macro-level studies { and especially cross-national com-

parisons { are an alternative way to resolve the fertility/employment puzzle

because they do not require the detailed individual-level data (see Rindfuss

and Brewster 1996, p. 262, who also stress the value of a cross-national as-

sessment). However, relationships at the individual and the aggregate level

may be di�erent (e.g., N�i Bhrolch�ain 1993).

Existing macro studies can be divided into studies which analyze macro-

level data on a cross-country basis and studies which apply methods of time-

series analysis. Various authors (Ahn and Mira 1999; Brewster and Rindfuss

2000; Esping-Andersen 1999; Rindfuss et al. 2000) �nd that in OECD coun-

tries the cross-country correlation between the total fertility rate (TFR) and

the female labor market participation rate (FLP ) turned from a negative

value before the 1980s to a positive value thereafter. The countries that now

have the lowest levels of fertility are those with relatively low levels of female

labor force participation and the countries with higher fertility levels tend

to have relatively high female labor force participation rates. Following the

graphical presentation in the literature (e.g., Rindfuss et al. 2000), Figure 1

illustrates this change for 12 selected OECD countries.1

Several recent papers have suggested a weakening link between fertility

and female employment due to greater availability of market child care, family

policies (such as state mandated maternity leave) and changing attitudes

towards working mothers (Brewster and Rindfuss, 2000, Rindfuss et al., 2000,

and Rindfuss and Brewster, 1996). For that reason, they argue that changes

in the institutional context at the macro-level must have enabled women in

some countries to better combine work and childrearing.

The cross-section studies, however, do not explicitly address the causality

question. This is done in studies which apply formal Granger causality tests

to aggregate time-series in di�erent countries (Cheng 1996; Klijzing et al.

1988; Michael 1985; and Zimmermann 1985). The basic logic underlying

these tests is quite simple: \We say, that [some time series] Yt is causing Xt

if we are better able to predict Xt using all available information than if the

information apart from Yt had been used" (Granger 1969, p.428). Causality

between two time-series can be either unidirectional (X causes Y or the

1Countries included are Belgium, Canada, Finland, France, Italy, Japan, Norway, Swe-

den, Switzerland, United Kingdom, United States and West-Germany until 1989 and

uni�ed Germany thereafter (excluding West-Germany -resp. uni�ed Germany- from the

sample leaves the graph almost una�ected). The data sources can be found in Appendix

A.

5

Figure 1: Correlation between the total fertility rate and female labor force

participation rate, 1960-1994

1960 1965 1970 1975 1980 1985 1990-1

-0.5

0

0.5

1

year

corr

elat

ion

coef

fici

ent

reverse), bidirectional (X causes Y and the reverse { this is termed feedback)

or non existent in which case the two time series move independently or

contemporaneously.

Table 1 provides a summary of empirical results of macro studies with

time series data. Analyzing German time-series from 1960-79 Zimmermann

(1985) concludes from a modi�ed Granger-causality test applied to �rst dif-

ferences of all variables that increasing female employment does not cause

decreasing fertility; rather the reduction in birth rate causes the increase in

female labor force participation. Applying standard Granger-causality tests

to the levels of US time-series data from 1948-80 Michael (1985) �nds that

female labor force participation positively causes fertility but not the other

way around. However, this result seems to be sensitive to the de�nition of

fertility. With age-speci�c fertility rates Michael �nds that fertility nega-

tively a�ects female labor force participation but not the other way around.

Klijzing et al. (1988) use aggregate data from a Dutch survey for a seven-

year period (1977-84) and apply Sims' indirect Granger-causality tests to the

�rst di�erences of the variables. They �nd that labor force participation has

no in uence on subsequent fertility decision-making and that fertility deci-

6

Table 1: Summary of macro-level time-series studies

author method data results

Zimmermann (1985) modi�ed Granger / German time series TFR ! FLP

�rst di�erences 1960-79

Michael (1985) standard Granger / US time series TFR FLP

levels 1948-80 AFR! FLP

Klijzing et al. (1988) indirect Granger / Dutch survey data FER! LFP

�rst di�erences 1977-84

Cheng (1996) modi�ed Granger / US time series TFR! FLP

�rst di�erences 1984-93

Notes: TFR { total fertility rate; FLP { female labor force participation rate;

AFR { age-speci�c fertility rate; FER { lagged (by 10 months) number of

children born (per month); LFP { percentage of women participating in the labor

market (per month).

sions do have an impact on female labor force participation. However, with

standard Granger tests they �nd causality in both directions. Cheng (1996)

applies a modi�ed version of the Granger-causality method to �rst di�erences

of aggregate US data for 1948-93. He �nds unidirectional negative causality

running from fertility to female employment.

Obviously, the time series literature has not yet found an agreement nei-

ther on the presence nor on the direction of causality between fertility and

female employment. In our view, this might be due to two issues that are

not yet addressed in the literature. First, the literature has not yet taken

into consideration several important recent developments in the econometric

time series literature (see section 4). In particular, Michael (1985) does not

consider non-stationarity of the time series, that is whether the mean and/or

the variance of the time series are changing over time. This is problematic

because, if the time series are non-stationary, then there is the possibility of

\spurious" causality results. Cheng (1996), Klijzing et al. (1988) and Zim-

mermann (1985) account for non-stationarity, but by only applying Granger-

causality tests to �rst di�erences, they refrain from the use of valuable infor-

mation about a possible long-run relationship between the variables.2 As a

2Though Cheng (1996) �nds absence of cointegration, i.e. absence of a long-run relation

between fertility and female employment, we have shown that these results are not robust.

While he uses the correct Granger-causality method given this result, he uses a unit root

test on the OLS residuals of the cointegrating relation. We applied an error correction

model to the same data and found cointegration. We believe this to be due to the well-

7

consequence, the results in these studies might be wrong.

Besides these methodological issues as related to the stationarity assump-

tion of the time series we allow for a further methodological correction. We

consider the possibility of parameter instability in the long-run relation be-

tween fertility and female employment (as suggested by inspection of Figure

1) and structural breaks in the trend of the variables. Clearly, it would be de-

sirable to include in the regressions socio-demographic variables that caused

this change in behavior. However, in our view this would be too complex {

if not impossible { and, for that reason, we approximate this change in be-

havior with the inclusion of dummy variables. The use of such a \minimal"

approach is a standard procedure in applied econometrics.

3 Data

We assemble annual time series from 1960-1994 of total fertility rate (TFR)

and female labor force participation rate (FLP )3 for �ve European coun-

tries (France (FRA), Italy (ITA), Sweden (SWE), West-Germany (FRG),

and United Kingdom (UK)) and the US.4 For FLP we choose the female

labor force divided by the female population both of age 15 to 64. Hence,

women of age 65 and older are not included in our measure of FLP . Clearly,

employment of these women (if at all existing) is not a�ected by fertility.

Excluding, additionally, women of age 50 and older might be desirable but

is not feasible due to data limitations. As a measure of fertility we use the

total fertility rate (TFR) which constitutes an age standardized measure of

fertility. It would be preferable to apply age standardized labor force partici-

pation rates, but data limitations do not allow for such an adjustment for all

countries in our sample. However, for some countries we have been able to

check whether using age standardised labor force participation rates instead

gives di�erent empirical results and could deny such a possibility.

In Figure 2 and Figure 3 we plot the time series of TFR and FLP .5 As is

known fact that error correction models are considered superior compared to the residual

based approach which tends to reject cointegration too often (see Kremers et al. 1992).3See Appendix A for de�nition and source of data.4For the time series of the Swedish FLP and the TFR of the USA one value for each

time series was missing. We calculated the missing value as the weighted average between

the following and the preceding data point.5In Figure 2 FRG denotes West-Germany for the entire sample. In Figure 3 FRG

denotes { due to data limitations { West-Germany until 1990 and uni�ed Germany after-

8

Figure 2: Time-series of the total fertility rate for six countries, 1960-94

1960 1965 1970 1975 1980 1985 19900

0.5

1

1.5

2

2.5

3

3.5

4

year

FRAFRGITASWEUKUSA

Figure 3: Time-series of female labor force participation rate for six countries,

1960-94

1960 1965 1970 1975 1980 1985 19900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

year

FRAFRGITASWEUKUSA

9

well-known, the time series of TFR show for most developed countries a kink

in the 1960s. Some researchers argue that this kink represents the di�usion

of the use of the contraceptive pill. Other researchers argue the kink is the

result of changing social norms. One can see that Italy is an exceptional case

since its fertility decline was very slow in comparison to most countries in the

developed world. The Swedish TFR shows a \miraculous" small hill around

1990. The demographic literature o�ers some explanations for this hill which

are, however, outside of the scope of our paper (see, e.g., Andersson, 1999,

and Hoem, 1990, who explain the increase of the Swedish total fertility rate

at the end of the 1980s with newly enacted leave and wage compensation

policies).

As is also well-known, the time series of FLP show a clear upwards trend

in most developed countries. Again Italy is an exception. There the rise

of female employment is rather modest. However, high education levels of

younger Italian women (not shown) seem to indicate a future change in the

FLP even in Italy. The Swedish FLP is distinguished by its relatively higher

level over the entire time period from 1960 to 1994.

We have opted to include Italy and Sweden in our set of countries since

each of them represents an extreme position in the spectrum of family poli-

cies and norms that may in uence the fertility/employment relation. The

exceptional behavior of the Italian time series is often explained with tradi-

tional norms and the view of the family as a private domain in which the

government does not intervene with many state services. On the other ex-

treme of a spectrum of family policy and norms is clearly Sweden. The policy

in the `nation of individuals' (Chesnais 1996; Hantrais 1997) tend to be both

supportive of women's desires and concerned with children's care. France

and the United Kingdom provide a somewhat weaker illustration of `nations

of individuals'. West-Germany as a `nation of families' shares a strong com-

mitment toward families, backed by monetary allowances for housing, child

bene�t packages, and well-paid maternal leave. To summarise: the time se-

ries in Figure 2 and 3 show that our set of six countries is representative for

most developed countries.

wards. However, in our empirical application in section 5 we use for (West-)Germany only

data for 1960-89 which excludes former East-Germany.

10

4 Econometric methodology

Before introducing the speci�c method we apply, we shortly review some

of the recent econometric time series techniques that need to be taken into

account when testing for causality.

Cointegration

When estimating with time series data the relation between two trend-

ing variables one often gets spurious regression results, that is, a seemingly

signi�cant e�ect even though the variables are actually unrelated. An illus-

trative example is the fertility rate and the number of storks in a region.

Both variables have mostly a downward trend. Due to their trends, when

regressing the number of storks on the fertility rate with OLS one might �nd

a signi�cant positive e�ect even though it would be daring to argue that such

a causal relation exists in reality. Often detrending (that is, including a trend

term as a further variable on the right hand side of the regression equation)

helps to eliminate spurious regression results. But as the recent econometric

literature (started by Granger and Newbold, 1974) shows, detrending does

not help in case the variables are di�erence-stationary, also labeled I(1). A

series is di�erence-stationary if its mean and its variance are constant over

time after �rst di�erencing.

Cointegration tests can be applied to detect whether a relation between

two I(1) variables is `true' or spurious. These tests aim to detect simultaneous

movements in deviations from the trend. More technically, cointegration tests

aim to detect whether there exists a linear combination of two I(1) variables

which is stationary (possibly after detrending). In case such a stationary

linear combination exists, the variables are said to be cointegrated and the

possibility of a spurious correlation due to trends can be excluded.

Granger-causality

Granger (1969) introduced tests to detect causality between time series

(henceforth labeled as Granger-causality test). The Granger causality test

is typically based on the estimation of a vector autoregressive (VAR) model

with variables in levels or in �rst di�erences:

11

�Yt = �0 +

mXi=1

�1;i�Yt�i +

nXj=1

�2;j�Xt�j + ut (1)

�Xt = �0 +

qXk=1

�1;k�Xt�k +

sXl=1

�2;l�Yt�l + vt; (2)

where �Zt = Zt � Zt�1; 8Z = Y;X; with all variables being in logarithms.

The �0s and � 0s are constants, m;n; q and s are the optimal numbers of

lags of the series Y and X and ut and vt are serially uncorrelated random

disturbances with zero mean. For given values of the lag lengths m;n; q and

s it can, for example, be tested, whether X Granger-causes Y by testing the

hypothesis H0: �2;1 = �2;2 = ::: = �2;n = 0 against the alternative Ha: not

H0. The joint signi�cance of the coe�cients can be tested by a Wald test

with the F-statistic.

Engle and Granger (1987) have shown that the Granger-causality test

can be seriously wrong if the time series are I(1) and cointegrated. For that

reason, we suggest to test �rst (with so-called unit root tests) if the variables

are I(1). If the variables turn out to be I(1), we suggest then to use a single

error correction model (ECM) to test for cointegration and causality upon

application of a method of Boswijk (1994).

Testing for cointegration in a single error correction model

An ECM can be tested with OLS and is written in the following form:

�Yt = �0 + �Yt�1 + Xt�1 + 't +

mXi=1

�1;i�Yt�i +

nXj=1

�2;j�Xt�j + ut; (3)

where the �0s; �; and ' are constants, t is a trend term and m and n are

again the optimal number of lags (we choose m and n so that the Schwarz

criterion is minimized, but limit m and n to a maximum of 2). Again, utis a random disturbance term with zero mean. Henceforth we include the

trend term in the ECM only if its coe�cient is signi�cant according to the

t-statistic (the t-statistic is reliable if Y and X are cointegrated).

Boswijk shows that one can test in (3) for cointegration between Y and X

with a joint Wald test of the hypothesis H0 : � = = 0: In this Wald test one

12

has to compare the �2-statistic that results from a test of H0 with the critical

values tabulated in Boswijk in Table B.1-B.5 (the tables are for various cases,

that is, with and without trend term in (3) and so forth). Cointegration is

accepted if the �2-statistic is larger than the relevant critical value.

Since our empirical results show that the time series of TFR and FLP

are cointegrated for each country included in our analysis, we restrict the

following exposition to causality tests in a single error correction model.

Testing for causality in a single error correction model

In case of cointegration, absence of weak exogeneity of X for Y implies

long-run causality of X for Y (Hall and Milne, 1994). A test for weak exo-

geneity in an ECM can be applied in two stages (Boswijk 1994). In the �rst

stage one may estimate the following equation with OLS:

Yt = + �Xt + �t + "t; (4)

where ; � and � are constants and "t is a random disturbance term with

zero mean. The relation in (4) is labeled as long-run relation between Y and

X. The residuals of the estimates of (4) (that is, �t = Yt � � �Xt � �t,

where a hat on top of a variable denotes the estimate of the corresponding

parameter) are saved and labeled as error correction term. In the second

stage the following equation is tested with OLS:

�Yt = �0

0+ �0�t�1 +

m0Xi=1

�0

1;i�Yt�i +

n0Xj=1

�0

2;j�Xt�j + u0t; (5)

where the (�0)0s and �0 are constants, �t�1 denotes the lagged error correction

term,m0 and n0 are again the optimal numbers of lags chosen according to the

Schwarz criterion and u0t is a random disturbance term with zero mean. The

variable X is weakly exogenous for Y , if �0 is insigni�cant according to the t-

statistic. Otherwise long-run causality (henceforth just labeled \causality")

of X for Y cannot be rejected. Intuitively, weak exogeneity implies that any

deviation in the long run relation between X and Y , i.e. �t 6= 0 for some t,

will impact on the value of �Yt.

Contrary to long-run causality, short-run causality of X for Y prevails if

13

in (5) the lags of �X are jointly signi�cant.6 However, in the subsequent

analysis we only test for long-run causality which also agrees with Granger

(1988) who questions the usefulness of the concept of short-run causality.

In addition to merely testing for causality between two time series one

may also test for parameter instability in the long run relation between TFR

and FLP .

Testing for parameter instability in the long run relation between

two variables within a single error correction model

To test for parameter instability one may estimate the following equation

with non-linear least squares (NLS) (the estimation procedure { but not the

test for parameter instability { follows Boswijk, 1994):

�Yt = �(Yt�1 � a� bXt�1 � � DUMtB Xt�1 � �t) (6)

+

eXi=1

�1;i�Yt�i +

fXj=1

�2;j�Xt�j + !t;

with DUMtB =

�1 if t > tB0 otherwise

;

where �; a; b; �; � and the � 0s are constants, e and f are optimal numbers of

lags chosen according to the Schwarz criterion and !t is a random disturbance

term with zero mean. tB denotes the possible date of a structural break in the

slope parameter of X. The hypothesis of a break in this slope parameter is

accepted if � is signi�cant according to the t-statistic. Inspired by a literature

that suggests methods to test whether a time series is di�erence-stationary

(see Maddala and Kim, 1998), we suggest to choose the date of a possible

break in the slope endogenously. More speci�cally, one may estimate (6) for

various values of tB and compare the corresponding t-statistics for testing

� = 0. The value of tB for which the absolute value of the t-statistic is

maximized may be chosen as the date of a possible break in the slope. In

case a break in the slope is accepted, we test the sign and the signi�cance of

the correlation between X and Y before the break and after it by testing the

6X is termed strongly exogenous for Y , if there is absence of short-run causality and

long-run causality ofX for Y and, in addition, u0t in (5) is uncorrelated with the disturbance

term in an to (5) equivalent equation with �Xt as the dependent variable.

14

following equation with NLS:7

�Yt = �[Yt�1 � a� b(DUM0 �DUMtB )Xt�1 (7)

�c(DUMtB �DUMT )Xt�1 � �t]

+

eXi=1

�1;i�Yt�i +

fXj=1

�2;j�Xt�j + !t;

where@Yt�1

@Xt�1

j long�run =

�b for t < tBc otherwise

;

and DUM0 = 1; 8t�[0; T ] and DUMT = 0; 8t�[0; T ], with the subscript 0

and respectively T as the dates at which the sample starts and respectively

ends. The (long-run) correlation between X and Y is signi�cant before the

break (resp. after the break) if b = 0 (resp. c = 0) is rejected according to

the t-statistic.

We have, for didactical reasons, deferred the exposition on how to test

for parameter instability to the end. However in practice one needs to test

for parameter instability �rst, in order not to distort the results of the coin-

tegration and causality tests.

5 Empirical application

Prior to any test of causality we apply the Augmented Dickey-Fuller unit root

test to the time series of TFR and FLP . These tests show that each time

series is di�erence-stationary. In the next step we test for instability in the

long run relation between TFR and FLP since parameter instability might

a�ect the causality test results. We estimate equation (6) for (i) �TFRt and

alternatively (ii) �FLPt as the dependent variable and test for an endogenous

break in the slope parameter as explained in the previous section. Table 2.a

summarizes the dates of breaks in the slope and suggests that for each country

the correlation between TFR and FLP has changed across time.8

7(7) is nothing else than (6) with the dummies rearranged. This rearrangement does not

change the content of the estimation results, but - in our view- simpli�es the interpretation

of the results. To give an example, in (7) the coe�cient in front of the term (DUM0 �

DUMtB)Xt�1 represents the coe�cient of the slope before the break (that is, from the

date of the start of the sample to the date of the break).8All endogenous breaks in the slope are signi�cant at the 5 % level.

15

Table 2.a: Endogenous dates of break in slope

Country/Dependent Variable �TFRt �FLPt

FRA 1973 1989

FRG(1960-89) 1976 1985

ITA 1987 1980

SWE 1980 1973

UK 1977 1986

USA 1976 1977

In addition, we �nd a signi�cant trend in the long run relationship be-

tween TFR and FLP for each country when we allow for breaks in the trend.

To start with we �rst make a guess of the possible dates for breaks referring

to the plots of the time series of FLP and TFR.9 To determine the exact

dates of the breaks we �nally choose them endogenously in the same way as

we choose the breaks in the slope parameter (that is, upon maximizing the

t-statistics of dummy variables).

Table 2.b: Endogenous dates of break in trend

Country/Dependent Variable �TFRt �FLPt

FRA 1978

FRG(1960-89) 1967,1976 1979

ITA 1964,1990 1975

SWE 1967,1980,1987 1967,1991

UK 1964,1971,1977

USA 1963,1970,1976,1986

The pattern of dates of breaks in the trend term can be summarized as

follows (Table 2.b). The TFR of each country contains a break that marks

the start of a downwards trend in the 1960s (as argued before presumably

due to changing social norms or the introduction of the contraceptive pill).

Moreover for most countries, the TFR series contain another break in the

1970s when the fertility decline stopped or became much weaker. On the

other hand, for three of the six countries the FLP has an upwards trend

9A guess of the date of breaks in the trend term in the �rst stage is a common practice

in tests of di�erence-stationarity of time series with possible non constant trends (see

Maddala and Kim, 1998).

16

without any break. For the other three countries a break marks the start of

an upwards trend in the FLP .

Next we test for cointegration between TFR and FLP by estimating

equation (3) for (i) �TFRt and alternatively (ii) �FLPt as the dependent

variable (we include the breaks in the slope and the trend term as indicated

in Table 2.a and 2.b). Table 3 summarizes the cointegration test results.10

Table 3: Test for cointegration between TFR and FLP

Country/Dependent Variable �TFRt �FLPt

FRA yes*** yes***

FRG(1960-89) yes* yes***

ITA yes*** yes***

SWE yes*** yes***

UK yes*** yes***

USA yes** yes***

Notes: *, **, *** 15 %, 5%, 1 % signi�cance level. \yes" means rejection of H0: no

cointegration.

Table 3 shows strong evidence for cointegration between TFR and FLP

for all countries. Hence, it is established that there is no spurious correlation

between TFR and FLP in aggregate time series data.

In order to test for the direction of causality between TFR and FLP

we use the two stage procedure as explained in the previous section. For

illustration, assume there is one break in the trend term of each time series.

In this case we estimate in a �rst stage the following equations with OLS:11

TFRt = �TFR+�TFR(DUM 0�DUM tB;TFR)FLP t

+

%TFR(DUM tB;TFR�DUMT )FLP t

+ (8)

#TFR(DUM 0�DUM tBT;TFR)(t=100)+

�TFR(DUM tBT;TFR�DUMT )(t=100);

10As suggested by the results in Table 2.a the coe�cient in equation (3) will in fact

be split up into two coe�cients 1 and 2 with the former (latter) one referring to periods

before (after) the structural break. In case 2 is not signi�cant we test for cointegration

on the joint hypothesis H0: (i) � = 0 in (3) and (ii) 1 = 0. However if 2 is statistically

signi�cant we apply the joint hypothesis H0: (i) � = 0 in (3) and (ii) 1 = 2 = 0.11In these equations the dummies for the trend are rearranged in the same way as

are the dummies of the slope in (7). E.g. in (8) the coe�cient in front of the term

(DUM0 �DUMtBT;TFR)(t=100) represents the coe�cient of the trend between the start

of the sample and the date of the break in the trend tBT;TFR.

17

FLP t = �FLP+�FLP (DUM 0�DUM tB;FLP )TFRt

+

%FLP (DUM tB;FLP�DUMT )TFRt

+ (9)

#FLP (DUM 0�DUM tBT;FLP )(t=100)+

�FLP (DUM tBT;FLP�DUMT )(t=100) ;

where �i;�i; %i; #iand �i 8i = TFR; FLP are constants, DUMtB;i ; 8i =

TFR; FLP denotes the break in the slope, DUMtBT;i ; 8i = TFR; FLP de-

notes the break in the trend with the subscript tBT;i indicating the date of

the break. As is the case in the cointegration tests, we include in the estima-

tions of equations (8) and (9) the breaks which are signi�cant according to

the estimations of (6). The residuals that result from estimation of (8) (resp.

(9)) are saved and used in the estimation of (5) with TFRt (resp. FLPt) as

the dependent variable. Table 4 summarizes the results of the tests for weak

exogeneity.

Table 4: Testing for causality between FLP and TFR

Country FLP ! TFR TFR! FLP

FRA yes*** yes**

FRG(1960-89) yes** yes*

ITA yes* yes**

SWE yes*** no

UK yes** yes***

USA yes*** yes*

Note: *,**,*** 15 %, 5 %, 1% signi�cance level. \yes" means rejection of H0: weak

exogeneity.

The table shows clear evidence of causality in both directions for all coun-

tries except Sweden (where it is only accepted that FLP causes TFR). In

our view, this �nding is consistent with simultaneous movements of both

variables brought about by common exogenous third variables. These third

variables are presumably �nancial incentives, social norms and institutions.

Finally, Table 5 shows the estimates of the long-run relation in the esti-

mation of (7), that is { for our illustrative example with one break in the

trend { for the TFR the term

TFRt�1 = a + b(DUM0 �DUMtB )FLPt�1 + c(DUMtB �DUMT )FLPt�1 +

#TFR(DUM0 �DUMtBT;TFR)(t=100) +

�TFR(DUMtBT;TFR �DUMT )(t=100) (10)

18

(and the same for the FLP ).12

Table 5: Estimation results of long-run relation

FRA

TFRt�1 = 0:20

�1:11���(DUM61�DUM 73)FLP t�1

�0:91�(DUM73�DUM 94)FLP t�1

(�2:38) (�1:83)

�1:23���(DUM61�DUM 78)(t=100)� 0:58

�

(DUM 78�DUM 94)(t=100);

(�3:63) (�1:95)

FLP t�1 = �0:50

�0:26���(DUM61�DUM 89)TFRt�1

�0:19���(DUM89�DUM 94)TFRt�1

(�7:56) (�6:76)

+0:27���(DUM61�DUM 94)(t=100):

(3:54)

FRG(1960-89)

TFRt�1 = 0:03

�1:22�(DUM61�DUM 76)FLP t�1

�0:40(DUM76�DUM 89)FLP t�1

(�1:72) (�0:53)

�0:36���(DUM67�DUM 76)(t=100);

(�6:62)

12As mentioned before, in our application we �nd for some countries more than one

break in the trend. The notation for the case with multiple breaks in the trend is a

straightforward extension of the notation used in the text (for example, the coe�cient

in front of the term (DUM64 � DUM78)(t=100) represents the coe�cient of the trend

from 1964 to 1978. Moreover, we exclude in the estimation equation the trend for a

particular time interval if in prior estimations the trend is insigni�cant for that time

interval (according to the 15% signi�cance level).

19

FLP t�1 = �0:68

�0:04���(DUM61�DUM 85)TFRt�1

+0:08��(DUM85�DUM 89)TFRt�1

(�3:24) (2:49)

+0:19���(DUM 79�DUM 89)(t=100):

(5:20)

ITA

TFRt�1 = 0:86

�1:06���(DUM61�DUM 87)FLP t�1

� 1:16���(DUM87�DUM 94)FLP t�1

(�13:64) (�14:59)

�1:96���(DUM64�DUM 90)(t=100)� 1:76

���

(DUM90�DUM 94)(t=100);

(�17:45) (�13:66)

FLP t�1 = �0:76

�0:38���(DUM61�DUM 80)TFRt�1

�0:56���(DUM80�DUM 94)TFRt�1

(�9:12) (�7:03)

0:55���(DUM75�DUM 94)(t=100):

(5:93)

SWE

TFRt�1 = 0:59

�0:42��(DUM61�DUM 80)FLP t�1

+1:14���(DUM80�DUM 94)FLP t�1

(�2:51) (3:44)

�1:19���(DUM67�DUM 80)(t=100) + 0:96

���

(DUM80�DUM 87)(t=100);

(�4:55) (3:33)

�1:19���(DUM87�DUM 94)(t=100);

(5:18)

FLP t�1 = �0:23

�0:38���(DUM61�DUM 73)TFRt�1

�0:20�(DUM73�DUM 94)TFRt�1

(�4:36) (�1:91)

+0:54���(DUM67�DUM 91)(t=100):

(4:87)

20

UK

TFRt�1 = 0:46

�0:81���(DUM61�DUM 77)FLP t�1

� 0:23�(DUM 77�DUM 94)FLP t�1

(�9:81) (�1:90)

�0:13���(DUM64�DUM 71)(t=100)� 0:26

���

(DUM71�DUM 77)(t=100);

(4:86) (13:41)

FLP t�1 = �0:66

�0:10���(DUM61�DUM 86)TFRt�1

�0:04(DUM86�DUM 94)TFRt�1

(�2:95) (�1:40)

+0:80���(DUM61�DUM 94)(t=100):

(8:18)

USA

TFRt�1 = �0:64

�0:65���(DUM61�DUM 76)FLP t�1

+0:07(DUM76�DUM 94)FLP t�1

(�3:81) (0:26)

�0:27���(DUM63�DUM 70)(t=100)� 0:33

���

(DUM70�DUM 76)(t=100);

(�5:07) (�9:11)

+0:29��(DUM86�DUM 94)(t=100);

(2:37)

FLP t�1 = �0:70

�0:14���(DUM61�DUM 77)TFRt�1

�0:07�(DUM77�DUM 94)TFRt�1

(�4:42) (�1:99)

+0:12���(DUM61�DUM 94)(t=100);

(13:62)

Notes: *,**,*** 15 %, 5 %, 1% signi�cance level, t-statistics in parenthesis and

DUMi =

�1 if t > i

0 otherwise; 8 i�[60; 94]:

21

Table 5 shows a signi�cant negative relation between TFR and FLP

before the break in the slope for all countries in all equations. Furthermore,

for each country the magnitude of this relation in the equation with TFRt�1

as the dependent variable exceeds the one in the equation with FLPt�1 as

the dependent variable. Table 6 summarizes for each country the change in

the relation between TFR and FLP after the break in the slope.

Table 6: Change of relation between TFR and FLP after the break in the

slope

Country �TFRt �FLPt

{ 0 + { 0 +

FRA x x

FRG(1960-89) x x

ITA x x

SWE x x

UK x x

USA x x

Notes: { indicates that the relation between TFR and FLP after the break is signi�cant

negative (at the 15% level) and its magnitude exceeds the one before the break ; 0

indicates that the relation between TFR and FLP is either signi�cant negative (at the

15% level) and weaker as compared to the period before the break, or insigni�cant (at

15%); + indicates a signi�cant and positive relation between TFR and FLP after the

break (at the 15% signi�cance level). For each country we indicate with a cross the valid

case.

Table 6 shows that in both equations (that is, with either TFRt�1 or

FLPt�1 as dependent variable) for four out of the six countries the negative

relation between TFR and FLP becomes smaller in magnitude or even in-

signi�cant after the break. However, the opposite holds for Italy where the

negative relation between TFR and FLP becomes even stronger after the

break.

To conclude, we �nd for all non-Mediterranean countries evidence for

a signi�cant negative relation between TFR and FLP before the break in

the slope and an insigni�cant or signi�cant negative, but weaker relation

after the break. This �nding is consistent with the view in Rindfuss and

Brewster (1996), Rindfuss et al. (2000) and Brewster and Rindfuss (2000)

that changes in childcare availability and attitudes towards working moth-

ers might have reduced the incompatibility between childrearing and female

22

employment. Moreover, our empirical results show that for Italy the relation

between TFR and FLP did neither become insigni�cant nor weaker (but

actually is signi�cantly negative and even bigger in magnitude as compared

to the period before the break) is consistent with the view in Brewster and

Rindfuss and Rindfuss et al. that in the Mediterranean countries there were

not such changes of family policies and/or social norms that reduced the

incompatibility between childrearing and work for women.

A glance at the time plot of the Italian FLP might even give an ex-

planation for our �ndings. The time series clearly reveals that in Italy the

FLP for women fell from 1960 to 1965. It might be that in the year 1960

(and possibly earlier) in Italy men's wage income was not enough to feed all

\mouthes" and so often women had to work to contribute \to make a living",

but could not restrict their fertility, for example, because at that time the

contraceptive pill was not introduced. As in the early 1960s the wage income

of the men grew, often women had not anymore to work to contribute \to

make a living" and, as a consequence, reduced their employment. Clearly,

such a mechanism would reduce the correlation between TFR and FLP in

the initial periods of our sample.

6 Conclusion

In this study we applied recent econometric time series techniques to test for

Granger-causality between fertility and female employment with macro-level

time series data of six developed countries. Compared to previous research we

introduced two new methodological elements: (i) we allowed for parameter

instability and (ii) we used an error correction model.

The existing literature mostly found unidirectional causation and con-

icting results on which is the direction of causation. In the light of our

empirical results { which show causality in both directions { we suggest that

previous research tended to reject causality too often. The failure to account

for parameter instability (either in the long-run relation between TFR and

FLP and/or the trend of each time series) may partly explain why previous

research rejected causality too often. Moreover many of the previous research

either ignored di�erence-stationarity of the time series (that is, did not test

for cointegration) or applied Granger-causality tests to the �rst di�erences

of the time series.

In retrospective of our result of causation in both directions, ignoring

23

di�erence-stationarity did probably not lead to wrong causality results since

this failure tends to �nd \spurious" causality rather than to reject causality

too often (indeed Michael, 1985, who applies Granger-causality tests to the

levels and ignores di�erence-stationarity { and does not allow for parame-

ter instability { �nds some evidence for causality in both directions). Of

course, one cannot know in the �rst place that there is no spurious causal-

ity problem. Therefore, testing for cointegration is imperative in case of

di�erence-stationary time series.

The application of a Granger-causality test to the �rst di�erences of the

time series is a special case of the application of an error correction model.

More speci�c, it is a Granger-causality test without the inclusion of the er-

ror correction term. However, not including the error correction term might

lead to serious problems because the error correction term contains the in-

formation about a possible long-run relation between fertility and female

employment. For that reason, Granger-causality tests applied to �rst dif-

ferences can only test for \instantaneous causation" and the information on

long-run causation is lost in this framework. From a statistical point of view,

this loss of information might be an additional explanation why the existing

literature tended to reject causality too often. From a substantive point of

view, if the correlation between fertility and female employment is the re-

sult of intentions (as, for example, economists would argue), then testing for

instantaneous causation is not useful. Clearly, if individuals \decide" about

their number of children, their timing of childbearing and their labor market

participation, then a respond to shocks takes time and, therefore, a test of

long-run causality seems much more useful.

Allowing for parameter instability not only prevented us from rejecting

causality too often. Omission of a break in the trend can also lead to biased

estimates of the coe�cient of the relationship between fertility and female

employment. Obviously, the same is true for the failure to account for insta-

bility in the correlation between fertility and female employment. Michael

(1985), for example, �nds a positive e�ect from female employment on fer-

tility with macro-level data. We also found in our empirical applications a

positive coe�cient for some countries when we did not account for structural

breaks (the results are not shown). Since we found for all countries a nega-

tive coe�cient before the break when we accounted for parameter instability,

empirical results that show a positive correlation between fertility and female

employment already in the 1960s and the 1970s might { in our view { indi-

cate biased estimates, where the bias is the result of failure to account for

24

parameter instability (it is possible that for Nordic countries the situation is

di�erent).

Besides the improvements of the estimation results, accounting for param-

eter instability is also an interesting �nding in its own right. Most impor-

tantly, allowing for instability of the correlation between fertility and female

employment revealed that for all non-Mediterranean countries the correla-

tion became weaker over time. This result with time series data complements

and supports recent studies which found for OECD countries that the cross-

country correlation between fertility and female employment turned from a

negative value before the 1980s to a positive value thereafter. Moreover, our

empirical �nding supports the view of a recent demographic literature which

argues that societal level responses reduced the incompatibility between fer-

tility and female employment.

25

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27

Appendix A: The data

1. TFR: total fertility rate

De�nition: Logarithm of children per woman of age 15 to 49 (for some

countries 15 to 44)

Data sources: The Demographic Yearbook of The United Nations

(1997), cd-rom (except West-Germany where the source is: German

Federal Statistical O�ce, section population and labor force).

2. FLP : female labor force participation in female population of age 15

to 64

De�nition: Logarithm of female labor force including female unem-

ployed divided by logarithm of female population of age 15 to 64

Data source: Comparative welfare states data set http://www.lis.ceps.lu/

28