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Does an effect of marriage duration on pre-transition fertility signal parity-dependent control?An empirical test in nineteenth-century Leuven,BelgiumJan Van Bavel aa Catholic University of LeuvenPublished online: 12 Dec 2010.

To cite this article: Jan Van Bavel (2003) Does an effect of marriage duration on pre-transition fertility signal parity-dependent control? An empirical test in nineteenth-century Leuven, Belgium, Population Studies: A Journal ofDemography, 57:1, 55-62, DOI: 10.1080/0032472032000061721

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Population Studies, Vol. 57, No. 1, 2003, pp. 55–62

ISSN 0032-4728 print/ISSN 1477-4747 online/03/010055-08 © 2003 Population Investigation CommitteeDOI: 10.1080/0032472032000061721

Does an effect of marriage duration on pre-transition fertility signal parity-dependent control? An empirical

test in nineteenth-century Leuven, Belgium

Jan Van Bavel

Catholic University of Leuven

It has been demonstrated for many pre-industrial populations that the age at marriage, or marriage duration,

influences age-specific marital fertility but the reason for this remains unclear. Among the several mecha-

nisms that may be responsible, the following are often cited: secondary sterility or increased subfecundity

associated with parity; declining coital frequency; the age difference between the spouses; and, importantly,

parity-dependent fertility control. If the latter mechanism were partly responsible for the marriage-duration

effect in pre-transition populations, it would contradict the concept of the modern fertility transition as the

evolution (or revolution) from parity-independent to parity-dependent fertility. The study presented in this

paper investigates the relative importance of these alternative explanations. The application of multivariate

Poisson regression to the fertility data from two birth cohorts in the Belgian city of Leuven shows that a

linearly declining or even concave age-specific fertility pattern, disaggregated by age at marriage, does not

imply parity-dependent fertility limitation.

Keywords:

fertility control; natural fertility; marriage duration; coital frequency; demographic transition;Western Europe; Belgium; historical demography

[Submitted April 2002; Final version accepted October 2002]

Louis Henry coined the concept of natural fertility asthe fertility a population would have if it did not useany form of control to limit the number of births(Henry 1953). Later, he specified that birth controlexists when the reproductive behaviour of couplesdepends on whether the number of children alreadyborn has reached the maximum number wanted(Henry 1961). Originally, Henry argued that naturalfertility was basically a function of woman’s age.Whenever a clear influence of age at marriage (ormarriage duration) was demonstrated, he interpretedthis as a sign of parity-dependent fertility controlbecause marriage duration could be considered aproxy for the number of children already born. In hislater work, however, he abandoned this view, as therewas growing evidence of the effect of marriageduration in supposedly natural fertility populations(Henry 1979, pp. 19–20).

Indeed, the effect of marriage duration on fertilityhas been demonstrated for many pre-industrial popu-lations but the reason for this effect remains unclear(Wrigley et al. 1997, pp. 392–4). Several mechanisms,all associated with marriage duration, may be

responsible. The following mechanisms are oftencited: secondary sterility or increased subfecundity inthe wake of earlier childbirth, declining coitalfrequency, the age difference between husband andwife, and, last but not least, parity-dependent fertilitycontrol (Knodel 1978; Blake 1985; Trussell and Wilson1985; Wilson et al. 1988; Bean et al. 1990, p. 132).

If, as suggested by Blake (1985), the latter mech-anisms were responsible for the marriage-durationeffect found in many pre-industrial populations, itwould contradict the concept of the modern fertilitytransition as the evolution from parity-independentnatural fertility to parity-dependent controlledfertility. Whether or not this is the case, however,remains a matter of speculation rather than demon-strated fact.

In spite of the importance of the issue, no researchhas been published, to our knowledge, that investi-gates alternative explanations of the marriage-duration effect empirically. This was the aim of thestudy presented here. It applies multivariate Poissonregression to the fertility data from two birth cohortsin nineteenth-century Belgium in order to investigate

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Jan Van Bavel

empirically whether or not the marriage-durationeffect signals parity-dependent fertility control.

Marriage duration and age-specific fertility

It has been common practice in historical demographyto use age-specific marital fertility rates to distinguishbetween natural and controlled fertility. In naturalfertility populations, these rates follow a convexfunction, while parity-specific fertility control causesthe rates to decline more steeply with woman’s age,forming a linear or even concave pattern (Coale andTrussell 1974; Wilson et al. 1988). Indeed, applicationsof this approach in pre-industrial populations almostinvariably found only small departures from theconvex, natural fertility pattern (Knodel 1977, 1978;Wilson 1984; Wilson et al. 1988; Wrigley et al. 1997).Exceptions were usually limited to special populationsof social forerunners (Livi-Bacci 1986).

However, many studies failed to control for age atmarriage (or marriage duration). Blake (1985)showed for some pre-transition populations that,when age at marriage is taken into account, age-specific fertility data that follow the ‘natural’ patternin fact exhibit the linear pattern supposedly typical ofcontrolled fertility. Specifically, she looked at someEnglish and French populations of the seventeenthand eighteenth centuries, and at a number of mid-nineteenth-century German villages (borrowing datafrom Wrigley and Schofield 1983; Dupâquier 1979;and Knodel 1978, respectively). Blake argued that itis the aggregation of different marriage durations inage-specific fertility rates that gives the artificialimpression of the natural, convex fertility pattern,while disaggregation by age at marriage reveals apattern typical of controlled fertility.

This is not always the case, however. For example,Wrigley et al. (1997, pp. 398–9) found that the clearmarriage-duration effect in England was limited to theperiod 1650–1749. In earlier and later periods (1538–1649 and 1750–1837), the effect was much weaker andnot entirely consistent. Furthermore, and an issue inthe present paper, the linear age-specific fertilitypattern within age-at-marriage groups does not neces-sarily signal deliberate fertility control (Wilson et al.1988). There are several alternative explanations.

One explanation refers to involuntary subfecun-dity or secondary sterility, that is, sterility broughtabout as a consequence of a birth or an abortion.Both were associated with considerable risks of infec-tion before modern health practices were adopted.Long marriage duration is positively associated withthe number of births and, hence, with the risk of

infection-induced subfecundity or secondary sterility.This causes the fertility rates to decline more rapidlywith age than in the expected convex pattern (Knodel1978; Trussell and Wilson 1985). Earlier analysis ofpre-transition family reconstitution data suggests,however, that the explanatory power of this mech-anism may be weak, at least in England. Wrigley etal. (1997, pp. 372–5) found that marriage duration orthe number of children born had a very limitedimpact on women’s risk of subsequent sterility.

A second, probably more important, alternativeexplanation of the departure from the convex patternmay be declining coital frequency at longer marriagedurations, unrelated to deliberate fertility control,and holding the age of both partners constant. Thereasons for this negative association have been givenscant attention by researchers. Of course, sexualabstinence is a possible strategy for fertility control,but coital frequency has been shown to be negativelyassociated with marriage duration even in theabsence of an intention to limit the number ofchildren (Wood and Weinstein 1988).

Knodel (1978) has suggested a third mechanismthat might help explain the negative effect of marriageduration on fertility, a reason related to the age of thehusband. It has been shown that, in European popula-tions before the fertility transition, women whomarried young tended to marry men who were consid-erably older, while women who married at older agestended to marry husbands of similar or younger age.‘Thus, for any given age of wife, husbands of womenwho married young tended to be older than husbandsof women who married at more advanced ages. Iffertility of women of a given age declines with the ageof the husband, this could help to account for theassociation between age at marriage and maritalfertility’ (Knodel 1978, pp. 497–8).

Whether or not these mechanisms do explain theeffect of marriage duration on age-specific fertility isan important issue for the concept of the fertilitytransition. If they cannot explain the whole durationeffect, and if it can be shown that pre-transitionmarital fertility was parity-dependent, then thefertility transition can no longer be viewed as achange of fertility regime from natural to controlled.In order to investigate the given alternative explana-tions, we introduce empirical indicators for thefactors that may be involved.

Methods

Historical demographers have detected fertilitycontrol indirectly from the difference between

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Effect of marriage duration on pre-transition fertility

57

observed age-specific fertility and the fertility to beexpected when couples’ reproductive behaviour doesnot depend on the number of children they alreadyhave. The more parity dependent the fertility control,the greater the difference between observed andexpected fertility. When the difference is consideredto be significant according to some standard or ruleof thumb, it is concluded that fertility is controlled.

Coale and Trussell (1974), building on the work ofHenry, argue that in the absence of fertility control,the general level of marital fertility varies but the agepattern follows a standard schedule. Parity-dependent fertility control causes fertility to divergefrom this model. The extent to which observed age-specific fertility differs from the standard patternindicates the extent to which couples control theirfertility. Let

r

(

a

,

i

) be the marital fertility rate at age

a

in population

i

. Then the Coale–Trussell modeldescribes it as follows:

r

(

a

,

i

) =

n

(

a

)

M

(

i

)

e

m

(

i

)

v

(

a

)

(1)

where

n

(

a

) is the standard age pattern of naturalfertility,

M

(

i

) the general level of fertility in popula-tion

i

,

v

(

a

) the standard schedule of age-specificfertility control effects, and

m

(

i

) the general level offertility control in population

i

. Hence, the Coale–Trussell model describes the difference between theactual and standard pattern by an age-specific vector

v

(

a

) on the one hand, and a population-specificparameter

m

(

i

) for the level of fertility control on theother (Xie 1990).

Whereas the Coale–Trussell model assumes thatfertility control is a function of age, the model ofmarital fertility developed by Page (1977) assumesthat it is a function of marriage duration. Like Henry,Coale and Trussell, Page assumes that

natural

fertilityis determined largely by woman’s age, but she arguesthat age is inadequate as a specification for thepattern of fertility

control

. ‘Control of fertility isusually taken to depend primarily on previousfertility experience: age cannot bear the samerelation to fertility experience in all populations,because the age at which women begin childbearingcan vary widely’ (Page 1977, p. 86). Duration ofmarriage is a more direct specification than age fordetecting patterns of fertility control, but age cannotbe discarded from a general model of marital fertilitybecause it remains an important physiological deter-minant of fertility. Page (1977) therefore proposes amodel incorporating both age and marriage duration.Let

r

(

a

,

d

,

i

) be the fertility of population

i

at age

a

and marriage duration

d

. The Page model implies thefollowing identity:

r

(

a

,

d

,

i

) =

n

(

a

)

M

(

i

)

e

d

β

(

i

)

(2)

In this model,

β

(

i

) represents the level of fertilitycontrol: it quantifies to what extent actual fertilitydiverges from the natural pattern when marriageduration

d

increases. The latter parameter is consid-ered to be a better proxy for parity than age.

In what follows, parity is introduced explicitly intothe model, together with age and marriage duration,in order to make it possible to decide on empiricalgrounds whether the marriage-duration effect is dueto parity-dependent fertility control. If, on the onehand, marriage duration does have an effect on age-specific fertility and parity does not, then neithersecondary sterility nor parity-dependent fertilitycontrol can explain the marriage-duration effect.Suppose, on the other hand, that we do find thatparity significantly affects age-specific fertility. Thenboth secondary sterility and parity-dependentfertility control might be present. The challenge is todistinguish between the two latter mechanisms.

In order to do so, fertility should be viewed fromthe perspective of reproduction, distinguishing netparity from crude parity. The former is the number ofchildren still alive at some point in time, while thelatter includes all children already born, those aliveas well as those who died. Hence, net parity equalscrude parity minus the number of children who died.If net parity has a statistically significant effect onage-specific fertility, even after controlling for crudeparity (or, equivalently, the number of children whodied), this would strongly suggest that fertility wasbeing controlled with the number of desired offspringin mind. If, on the other hand, only marriage durationand crude parity affect marital fertility significantlyand net parity does not, then declining coitalfrequency and secondary sterility are sufficient toexplain the departure from the standard convexscheme. In that case the marriage-duration effectwould manifestly not imply fertility control.

The inclusion of crude parity is essential for theanalysis in order to control for two opposing mech-anisms behind the bivariate association between thenumber of children already born and subsequentfertility. On the one hand, we expect a positiveassociation between crude parity and fertility becauseparity, at a given age and marriage duration, is posi-tively associated with fecundability. The higher thefecundability, the shorter the interbirth intervals, andthe higher the crude parity attained. On the other hand,every birth entails some risk of secondary sterility orsubfertility, implying zero or lower sub-sequentfertility. Of course, the relation between crude parityand secondary sterility is more complex, because

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selection effects are at work as well: women whobecome secondarily sterile at some lower parity willnever reach a higher parity. At issue here, however, isthe explanation of the effect of marriage duration onfertility. The literature suggests that the effect may bedue, to some extent, to sterility induced by childbearing.Thus if marriage duration still affects fertility signifi-cantly after controlling for parity, then that durationeffect cannot be explained away by secondary sterility.

Because net parity equals crude parity

minus

thenumber of children who have died, the effect of netparity on the fertility rate, after controlling for crudeparity, is exactly the opposite of the effect of thenumber of children lost. To some extent, then, wewould be measuring the effect of infant mortality onfertility, which is known to be positive even in theabsence of fertility control (Preston 1978). Thiswould blur or even invalidate the analysis becausenet parity was included in order to detect parity-dependent fertility control while in fact it would becapturing an infant mortality effect as well. There-fore, we should also control for that effect. Thefollowing analysis does this by including a dummyvariable that represents the survival or death of theprevious child. Finally, the age difference betweenthe spouses is introduced into the analysis to assessthe importance of that factor.

Because of the introduction of crude parity, netparity, infant survival, and the age difference betweenthe spouses into the age-specific and duration-specificanalysis, it is no longer feasible to model fertility atan aggregate level. Rodriguez and Cleland (1988)showed how the Coale–Trussell and the Page modelcan be reformulated at the individual level, allowingmore factors to be introduced in a multivariate anal-ysis. Following their Poisson approach, and extendingthe Page model, marital fertility can be written as afunction of a vector

X

of

k

characteristics of marriage

i

observed at woman’s age

a

:

r

(

a

,

i

) = = µ ·

n

(

a

) ·

e

β

kXk

(

a

,

i

)

(3)

⇒

log

B

(

a

,

i

) = log

P

(

a

,

i

) + log µ + log

n

(

a

)

+

X

k

(

a

,

i

)

β

k

where

B

(

a

,

i

) is the number of births in marriage

i

atthe wife’s completed age

a

, and

P

(

a

,

i

) the corre-sponding exposure time (or time at risk). The unknownparameters in the model are µ, the general level offertility in the population, and the vector

β

containingthe

k

effect-parameters of the individual covariates. Inthe following regression analysis, these covariates aremarriage duration, crude parity, net parity, a dummy

representing death or survival of the previous child,and the age difference between the spouses. Clearly,some of these are highly correlated, but this does notjeopardise the validity of the analysis as long as we haveno perfect multicollinearity (Berry 1993).

Data

The model described in equation (3) will be appliedas a Poisson regression to the fertility data collectedfor two nineteenth-century generations living in theBelgian provincial town of Leuven. This was a Dutch-speaking traditional trades and crafts centre with aFrench-speaking bourgeois elite. The first generationconsists of all married couples with at least one of thespouses born in 1830 and who had ever lived inLeuven between 1847 and 1880. The second genera-tion includes all couples with man or wife born in1864 and who had ever lived in the same townbetween 1881 and 1910. These two generations werechosen in such a way that the first completed itsfertile life course before any signs of marital fertilitydecline were visible at the aggregate level. Themarital fertility transition started in Leuven in theearly 1880s, when the second generation was reachingadulthood. The data were collected for the period1846–1910 from the population registers and fromcivil registration records (birth, death, and marriagecertificates). Gutmann and van de Walle (1978) andLeboutte and Obotela (1988) describe the generalcharacteristics of these sources. Van Bavel (2002)describes the Leuven sample in detail. Table 1 givessample size information: the observed number ofperson-years by age and generation.

Table 1 also gives the marital fertility rates andmaximum likelihood estimates of the parameters

M

and

m

in the Coale–Trussell model, fitted to the datafollowing the Poisson regression approach (Broström1985). Analysis of the age-specific fertility ratessuggests that, according to the conventional interpre-tation (Coale and Trussell 1974, 1978), the first gener-ation did not control fertility in a parity-dependentway (

m

= 0.077), while the second generation startedto exhibit a pattern typical of parity-dependentfertility control (

m

= 0.472). It has been shown,however, that the Coale–Trussell model is incapableof detecting small but significant proportions of thepopulation who are controlling their fertility (Okun1994). Hence, a minority of the oldest generation mayalready have been limiting births.

In addition, breaking down these age-specific ratesby age at marriage yields a pattern that suggests theexistence of fertility control in the oldest generation

B a i,( )( )P a i,( )( )---------------------

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Effect of marriage duration on pre-transition fertility 59

as well: already in the 1830 generation, maritalfertility rates decrease linearly with woman’s age,controlling for her age at marriage. This can be seenin Figure 1, and an analysis using the Page modelconfirms the visual impression: maximum likelihoodestimation of the β(i) parameter in equation (2)yields values that differ significantly from zero in theoldest as well as in the youngest generation,suggesting deviance from the natural fertility patternin both cases (Page 1977; Van Bavel 2002, pp. 98–104). The aim of the following multivariate regressionanalysis is to see whether this pattern does in factindicate parity-dependent fertility control.

The dependent variable r(a, i) is the number ofbirths to marriage i at completed age a, divided by thenumber of person-years marriage i was observed inLeuven. Age is measured here in 1-year age intervals,

not in 5-year categories, starting from the wife’s 20thbirthday. As a consequence, the numerator of thedependent variable hardly ever exceeds one, becausegiving birth more than once a year is exceptional. Thedenominator equals one when a marriage wasobserved during a full year. In case of censoring, thedenominator is a fraction of one. Marital duration isexpressed in the number of completed years,measured at the exact age a of the wife. The age differ-ence between man and wife is expressed in exactnumber of years. Net parity is known only for coupleswho had remained under observation in the Leuvenpopulation registers from the start of the marriage.Hence, left-censored cases had to be excluded fromthe regression. After this exclusion, 3,071.6 person-years were still available for analysis from the firstgeneration, and 4,448.9 person-years from the second.

Findings

As explained by Rodriguez and Cleland (1988),equation (3) describes a type of model that falls in theclass of generalised linear models. An importantimplication is that maximum likelihood estimation ofthe unknown effect-parameters is possible, yieldingestimates of the standard errors and the likelihoodratio statistic also (Long 1997). The results of thisfitting procedure, applied to the Leuven cohort data,are given in Table 2.

Judged by any conventional standard, the modelfits the observed fertility data quite well for bothgenerations. The bottom of Table 2 gives goodness-of-fit statistics, namely deviance and the Bayesian

Table 1 Number of person-years observed, age-specific marital fertility rates, and maximum likelihood estimates of the Coale–Trussell parameters, for two nineteenth-century generations in Leuven (Belgium)

1830 generation1 1864 generation2

Woman’s age P(a)3 Fertility rater(a)

P(a)3 Fertility rater(a)

20–2425–2930–3435–3940–4445–49Coale–Trussell model

386.96866.80

1,150.961,193.251,024.20

889.65M = 0.904

0.4080.3920.3340.2720.1440.021m = 0.077

688.651,433.211,702.231,582.631,270.87

441.75M = 0.851

0.4020.3200.2540.1540.0800.023m = 0.472

1Couples with one spouse born in 1830.2Couples with one spouse born in 1864.3P(a) = exposure, or the number of person-years observed in the age interval.Source: Population registers and civil registration records (Van Bavel 2002).

Figure 1 Age-specific marital fertility by generation and woman’s age at marriage, Leuven (Belgium), 1846–1910Source: As for Table 1

Woman’s current age

Mar

ital

fer

tili

ty r

ate

0.6

0.5

0.4

0.3

0.2

0.1

0.0

1830 generation

1864 generation

20-2425-29

30-3445-4935-39

40-4440-44

25-2930-34

45-4935-39

A Women married at age 20 to 24 B Women married at age 25 to 29

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60 Jan Van Bavel

information criterion (BIC). The latter measure iswidely used because it takes into account both thedeviance, that is, the difference between observedand predicted data, the parsimony of the model, andthe sample size. Negative BIC values indicate that themodel is statistically acceptable (Long 1997, pp. 109–12), which is clearly the case here.

Figure 2 gives a visual impression of the fit. Itgraphs observed and predicted fertility rates bywoman’s age and by marriage duration. Observedrates are somewhat erratic because of sampling error,but the model predicts the pattern quite well. Thereis one systematic difference between observed andmodel rates: as has already been noted by Rodriguezand Cleland (1988), the model tends to overestimatefertility in the year immediately following firstmarriage and to underestimate it a year later. It ismost probably a consequence of the special nature ofthe first year of marriage, in which fertility tends tobe high but which represents substantially less than afull year of exposure time. Anyway, the difference

between observed and predicted fertility rates duringthe first 2 years of marriage tends towards self-compensation (as in Rodriguez and Cleland 1988)and is not important for present purposes.

The first and most important conclusion that canbe drawn from the regression results is that thenegative effect of marriage duration on fertility canclearly not be explained away by the effects ofsecondary sterility and parity-dependent fertilitylimitation. Indeed, even after controlling for crudeand net parity, marriage duration has a strong andstatistically significant effect on marital fertility. Table2 gives the regression parameters in an exponenti-ated form in order to make them substantially inter-pretable as a factor-effect-parameter. The estimatedeffect of marriage duration in the 1830 generationimplies that, on average and holding other factors inthe model constant, fertility decreased by a factor of0.953, or by about �5 per cent, for each additionalyear a marriage lasted. In the 1864 generation,fertility went down with marriage duration about

Table 2 Poisson regression of age-specific marital fertility of two generations: effects of marriage duration, the age difference between the spouses, crude and net parity, and death of the lastborn infant, Leuven, Belgium, 1846–1910

1830 generation 1864 generationecoeff. s.e. p ecoeff. s.e. p

Overall marital fertility levelMarriage durationAge difference (husband – wife)Crude parityNet parityPrevious infant died (1 = Yes, 0 = No)

DevianceBIC

0.8570.9530.9961.1220.9701.555

1,885.2�23,621

0.0740.0120.0060.0390.0450.104

df3,164

0.0355<0.0001

0.45450.00310.4919

<0.0001

N1

3,170

0.6800.8990.9971.3000.9061.569

2,557.4�36,348

0.0650.0100.0070.0370.0450.099

df4,611

<0.0001<0.0001

0.7151<0.0001

0.0281<0.0001

N1

4,617

1 N = number of age intervals in the sample.Source: As for Table 1.

Figure 2 Observed and fitted age-specific and duration-specific marital fertility ratesSource: As for Table 1

Woman’s age

Fer

tili

ty r

ate

0.5

0.4

0.3

0.2

0.1

0.0

1830 generation observed

1830 generation model

1864 generation observed

1864 generation model

20 25 30 4035 5045

Marriage duration

Fer

tili

ty r

ate

0.5

0.4

0.3

0.2

0.1

0.0

1830 generation observed

1830 generation model

1864 generation observed

1864 generation model

0 5 10 15 2520

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Effect of marriage duration on pre-transition fertility 61

twice as fast (0.899 or �10 per cent for each addi-tional marriage year).

The effect of the age difference, if any, between thespouses was statistically significant in neither of thetwo generations after controlling for the other covari-ates. Other specifications of the age difference weretested, including categorical and non-linear ones, butnever yielded a significant effect. The regressionparameter for age difference becomes significantonly after the deletion of crude and net parity fromthe model. Indeed, age difference is highly associatedwith the parity reached: women who marry relativelyearly tend to marry older men. This group alsoreaches the highest parities. Women who marry rela-tively late tend to marry younger men but do notreach high parities. Thus, the suggested effect of agedifference on fertility may be spurious.

Crude parity has a positive effect on age-specificmarital fertility in both generations: for a given ageand marriage duration, the marriages that are subse-quently more fertile are the ones that were morefertile in the past. In other words: holding everythingelse constant, women who already had given birth toan above-average number of children had an above-average number in the future, presumably because ofhigher fecundability or restricted breastfeeding. Tobe sure, these are the women who had run the highestrisks of becoming secondarily sterile as well. In short,given the effect of marriage duration after controllingfor parity, duration had an effect in both generationsthat cannot be reduced to the effect of secondarysterility.

Clearly, it can also not be reduced to the effect ofparity-dependent fertility control. As explainedabove, the model includes net parity in order todetect fertility control in both generations. Accordingto the estimators given in Table 2, fertility did notdepend significantly on the number of children alivein the first generation. In the second generation, itdid, even after controlling for the survival of theprevious infant. The effect of the death of the previ-ously born infant was the same in both generations:it increased fertility by about 55 per cent. Asexplained above, controlling for this natural fertilitydeterminant is essential in order to allow the effect ofnet parity to be interpreted as fertility control.Indeed, if the infant survival dummy is deleted fromthe regression (as was done in Van Bavel 2002, butnot shown in Table 2), the coefficient for net paritybecomes statistically significant in the first genera-tion, spuriously suggesting parity-dependent fertilitycontrol. In fact, there was no parity-dependentfertility control in the first generation. In sum, thenegative relationship between marriage duration and

age-specific fertility did not signal fertility control, atleast not in the pre-transition population of Leuven.

Conclusion

Bean et al. (1990) state that no single explanation canbe provided for the relationship between age atmarriage and fertility. Like Wilson et al. (1988),among others, they posit three plausible explana-tions. ‘These include the possibility of reduced coitalfrequency associated with duration of marriage andincreased subfecundity associated with parity, as wellas the adoption of some limited form of parity-dependent family limitation. If the latter condition ispresent, then the applicability of the concept of“natural fertility” to the population must be ques-tioned’ (Bean et al. 1990, p. 132). Further, Knodel(1978) includes the age difference between spousesin his list of plausible explanations. The relativeimportance of these alternative mechanisms hasnever been weighed empirically in a pre-transitionalpopulation. The application of a Poisson regressionanalysis to marital fertility data from a pre-transitionbirth cohort suggests that even a strong marriage-duration effect by no means has to imply parity-dependent stopping behaviour. Marriage durationhas a negative effect on fertility that cannot bereduced to the combined effect of parity-dependentcontrol, secondary sterility (or subfecundity), and theage difference between spouses. The most importantcausal mechanism at work seems to be what CharlesF. Westoff has described as ‘the saddest curve in theworld’: the decline of coital frequency associated withincreasing marriage duration. If these results can bereplicated for other pre-transition populations, thenthe claim made by Blake (1985), that ‘the rates dis-aggregated by age at marriage suggest possiblefertility control after a given number of births’, willfinally be overruled on empirical grounds.

Note

1 Jan Van Bavel is at the Department of Sociology, Facultyof Social Sciences, Catholic University of Leuven, VanEvenstraat 2B, B-3000 Leuven, Belgium. E-mail:Jan.VanBavel@soc.kuleuven.ac.be

This paper was written as part of a research projectsupported by the Flanders National Fund for ScientificResearch (F.W.O. – Vlaandeven). For their comments onsome of the arguments made in this paper, the authorwishes to thank Ron Lesthaeghe, Koen Matthijs, MichelOris, Frans Van Poppel and Bart Van de Putte.

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