To explore the effects of real wages and parity on fertility responses, we estimate the hazard rates of four different events: (1) marriage; (2) first conception (“starting”); (3) conception following the previous birth (“spacing”); and (4) last conception (“stopping”), for which the date of a conception is set 40 weeks prior to the date of a birth.Footnote 4 The unit of observation in the marriage, starting, and stopping analyses is the wife. The outcome variable here measures the time span from when the wife becomes at risk until the relevant event occurs.Footnote 5 In the marriage, starting, and stopping analyses, where the relevant events are the marriage, the first conception, and the last birth, respectively, the unit of observation is the family (i.e., there is one observation per family), and the family is considered to be at risk from the point in time at which the wife reaches the age of 15. In the spacing analysis, where the relevant event is the conception following the birth of the previous child, the unit of observation is the birth interval (i.e., there are potentially multiple events per family), and the wife is considered at risk of conceiving her next child at the birth of the previous child. The outcome variable is, therefore, the time span from the date of birth or baptism of one child until the date of conception of the subsequent child. The date of conception is calculated by subtracting nine months from the date of birth or baptism. In our analysis, we consider only closed birth intervals.Footnote 6
Of note is that 90 % of our sampled birthdates are inferred from baptism dates. Previous studies have shown that most children were baptized within one month of birth (Midi Berry and Schofield 1971). Yet, a potential problem is that the time elapsed between birth and baptism may have differed systematically over time, across the sampled parishes, and across occupational groups. However, because our estimates are either based on variation within families or stratified by parish and quarter-century, such differences are accounted for.
In regressions investigating parity-independent birth spacing, each of the four events is regressed on national real wages for each of the years over the modeled interval.Footnote 7 Furthermore, dummy variables indicating the order of surviving births (here denoted “net parity”) are included in regressions investigating parity-dependent birth spacing.Footnote 8 We control for the income class of the husband based on his occupation; the wife’s age at marriage;Footnote 9 the wife’s age at the beginning and during the birth interval;Footnote 10 the wife’s literacy status;Footnote 11 and a proxy for the couple’s fecundity (i.e., capacity to conceive) measured by the time elapsed between marriage and first birth (i.e., the protogenesic interval). To capture the possibly nonlinear association between fecundity and age, we include a quadratic polynomial of maternal age that varies during the birth interval. We also account, again in a time-varying fashion, for the death of the previous child before the next conception. Finally, as is common in the literature, we include a binary variable for the last birth interval to capture a failed attempt to stop having children (Anderton 1989; Knodel 1987; Okun 1995; Van Bavel 2004a).Footnote 12
We estimate a time-varying Cox proportional hazard model (Cox 1972) specified as follows:
$$ h(t)={h}_o(t) \exp \left({\upbeta}_1{x}_1+{\upbeta}_2{x}_2+\cdots +{\upbeta}_k{x}_k+ g(t)\left(\upgamma W\right)\right). $$
(1)
The term h
o
(t) is the baseline hazard function where t is time, measured in days; (x
1, . . . , x
k
) are socioeconomic and demographic covariates; and W is the standardized (zero mean and unit standard deviation) time-varying (yearly) real wage (Clark 2007). In all our analyses, we stratify by parish and quarter-century: that is, each parish and quarter-century provides unique baseline hazard functions. With this stratification, our analyses account for the heterogeneity between different time periods and locations. The stratification by quarter-century furthermore implies that the estimated impact of real wages on birth intervals can be interpreted as a short-term effect. Finally, although demographic events are recorded on specific dates, the real wages are annual averages, and so our standard errors are clustered by the year of the demographic event considered.Footnote 13
Parity-Independent Birth Spacing
Table 3 reports the estimates of our duration models capturing the effects of the real wage and the control variables on the duration to each of the studied events. Real wages are standardized with a mean of 0 and a standard deviation of 1. To ease comparison with previous studies, we report hazard ratios.
Table 3 The impact of the real wage on marriage, starting, spacing, and stopping
Column 1 of Table 3 establishes that the real wage is positively and significantly correlated with the hazard of marriage. This is prima facie evidence of a direct negative effect of living standards on the wife’s age at marriage, supporting the Malthusian hypothesis that delayed marriage was a response to hard times as well as a sign of the existence of a preventive check mechanism operating among the sampled population in pre-transitional England.
Column 2 focuses on the event of giving birth to the first child within marriage (“starting”). The estimates indicate a positive and statistically significant correlation between the real wage and the protogenesic interval. The magnitude of the effects on the events of marriage and starting are very similar: a 1 standard deviation increase in the real wage accelerates time to marriage and to first conception by 23 % and 25 %, respectively. This is consistent with the conventional view that marriage historically marked the onset of a family (i.e., to give birth).
The estimates in column 3 present evidence of pretransitional, parity-independent birth spacing, establishing that an increase in real wages accelerates the timing of the next conception. The magnitude of the impact of the real wage is also economically significant: a 1 standard deviation increase in the real wage accelerates the timing of the next conception by approximately 10 %.Footnote 14
Turning to the stopping specification (column 4), we find no statistically significant impact of real wages on the hazard of the last conception. The effect remains statistically insignificant when we consider starting ages other than 15 for the event of stopping and when we split the sample by 50-year subperiods (not reported). These results are perhaps unsurprising: because real wages are largely nontrending across the period under observation, short-term variations in real wages are likely to cancel out over the course of a family life cycle, leaving little room for wages at any point in time to substantially affect the timing of the last birth.Footnote 15
In summary, our analyses establish that falling living standards captured by lower real wages led not only to significantly later marriages but also to longer birth intervals within marriage. In our robustness analyses, we explore the impact of some key confounding factors to rule out the possibility that the spacing effects we observe are positive checks rather than preventive checks.
Socioeconomic Factors and Other Covariates
To shed light on the role of socioeconomic factors in historical birth patterns, we subdivided our sampled families into income groups using a categorization proposed by Clark and Cummins (2015). Clark and Cummins used information about male testators to group male occupations according the amount of wealth left in the will. From poorest to richest, these groups are laborers, husbandmen, craftsmen, traders, farmers, merchants, and gentry. Our reference group in the analysis is laborers (the poorest group in the classification scheme). Concerning the hazard of a marriage, apart from craftsmen—who tended to marry later in life than others—none of the groups differ significantly from laborers (Table 3, column 1). When looking at the timing of the first birth, craftsmen—but also farmers—had their firstborns comparatively later in life (column 2).
More interestingly, looking at birth spacing, we find that poorer families had longer birth intervals on average than richer ones: column 3 shows that all six occupational groups included in the model have significantly shorter birth intervals (higher hazard ratios) compared with the reference group (laborers). In particular, we find that the coefficients for the richest groups (traders, farmers, merchants, and gentry) are statistically different from the coefficients of husbandmen and craftsmen; the difference between husbandmen and craftsmen is not statistically significant. Therefore, birth intervals appear to decrease with wealth.
The mechanism causing these differences in birth intervals between rich and poor may have to do with differences in breast-feeding practices. Women in poor families would breast-feed their own children, but the rich could afford to pay a wet nurse, explaining why the more-affluent social groups display a larger hazard of a further birth (Fildes 1987). Differences in the practice of coitus interruptus may also explain the different patterns of birth spacing (Santow 1995).
We also find a large impact of a child death on the next conception, with a child death accelerating the timing of the next conception by some 74 %. Possible reasons for this effect include the interruption of the breast-feeding period (which shortens postpartum amenorrhea) and the attempt to replace the deceased child.
Interestingly, socioeconomic differences also apply in the case of stopping. Column 4 establishes that, on average, laborers stopped later than their more-affluent counterparts and that the gentry were more likely to stop earlier. Husbandmen, craftsmen, traders, and merchants also stopped significantly earlier than laborers. These results are conditional on the mother’s age at marriage, her age at the last birth, and the family size. In fact, we find that a larger family size was associated with a later time of stopping. Therefore, differences in sterility associated with differences in the age at marriage or family size cannot explain the differences in stopping practice across occupational groups. The fact that the rich had more surviving offspring than the poor, as demonstrated by Clark and Hamilton (2006) and Boberg-Fazlic et al. (2011), can thus be ascribed to earlier starting and shorter birth intervals. The earlier stopping pattern among the rich (especially gentry) is consistent with the notion that wealthier families may have had a target number of offspring (for a discussion, see Van Bavel 2004a).
Literacy among wives is also associated with shorter birth intervals and earlier stopping age, even after we control for socioeconomic status. Perhaps literate individuals from the lower socioeconomic ranks imitate the fertility patterns of their higher socioeconomic counterparts. Moreover, couples of low fecundity, captured by a relatively large protogenesic interval, had (as expected) significantly larger birth intervals than couples of high fecundity. Also, the group of couples that gave birth to children within 40 weeks of marriage (which includes couples that conceived their firstborn before marriage) had an overall lower hazard of subsequent births. The latter finding seemingly contradicts the suggestion made by Wrigley et al. (1997:422) in their description of the data’s prevalence of prenuptially conceived births: “It might be expected that such women [giving prenuptially conceived birth] would display higher fertility during the balance of their childbearing life than women whose first child was born more than nine months after marriage, since it might be supposed that women of high fecundity, or perhaps with a greater appetite for sexual activity, would have higher fertility and would be more likely to become pregnant before marriage than others.”
Last, as documented in previous studies, we find that the last birth interval was significantly larger, on average, than the previous intervals. This finding is consistent with the idea that the last birth was sometimes a failed stopping attempt.
Before we proceed to explore the role of parity in detail, it is useful to take a preliminary look at the variable birth order. The coefficient for birth order (Table 3, column 3) is highly statistically significant and suggests that higher parities are associated with shorter spacing. As discussed in the Introduction, this finding may arise from a selection bias stemming from the use of variation in birth spacing across families rather than within them. That is, as we move from lower to higher birth orders, the composition of the sampled families may shift toward a higher share of more-fecund couples, and hence couples of shorter-than-average spacing. As the birth order results of Table 3 indicate, the composition effect may lead us to mistakenly conclude that higher parities were associated with shorter spacing of births. However, given the nature of our data, this issue of selection bias can be addressed by accounting for between-family heterogeneity. To shed light on these matters, the next section explores variation in birth spacing across families as well as within them.
Parity-Dependent Birth Spacing
This section is devoted to the question of whether birth spacing depended on the stock of surviving offspring in a family. More specifically, we test the hypothesis that the timing of a successive birth is independent of the number of children already born (e.g., Henry 1953). We conduct the test similar to those in previous studies (e.g., Bengtsson and Dribe 2006; Van Bavel 2004a) by estimating parity fixed effects. In particular, we define net parity as the number of children alive at the start of the interval and include in the model a dummy variable for each net parity. Importantly, to test for parity-specific birth spacing appropriately, we also account for between-couple heterogeneity: that is, the fact that highly fecund couples are able to have shorter birth intervals, on average, and hence can reach higher parities, causing a potential selection bias toward shorter spacing at higher parity. We account for this selection bias by stratifying our sampled birth intervals on the family level.
Table 4 presents the estimates from duration models of birth intervals with and without stratifying on the family level. The different estimates reported in columns 1 and 2 of Table 4 illustrate the relevance of stratifying on the family level, indicating also the main reason for why our findings deviate from those of the Cambridge Group (e.g., Wrigley et al. 1997). Column 1 reports the results of using our previous spacing model augmented with only parity fixed effects. In this specification, we stratify the model by parish and quarter-century and control for the wife’s age at the beginning and during the birth interval (using a linear and a quadratic term) to capture age-related variation in maternal fecundity: we do not stratify by family.
Table 4 Parity-dependent birth spacing
The findings reported in column 1 of Table 4 show that the speed of a successive conception is significantly lower at parity 2 or higher compared with the reference group (parity 1). In addition, the difference between parity 2 and the remaining (higher) parities is statistically the same. This latter result is consistent with the Cambridge Group’s finding that “birth interval lengths changed very little between parities 2 and 5” (Wrigley et al. 1997:435). Our latter finding would therefore support the natural fertility hypothesis in that the spacing of births (after parity 1) does not appear to depend on parity.
Column 2, instead, reports the results when we account for heterogeneity among the sampled couples, stratifying by family and quarter-century. We stratify also by quarter-century to allow the baseline hazard to vary over time.Footnote 16 By using variation in birth spacing within families, we find that the speed of a successive conception decreases monotonically with net parity, meaning that the spacing of births increases monotonically with net parity. For example, the coefficient for “Net parity 2” implies that the time to the successive conception after the second sibling is approximately 52 % lower than after the first sibling; the time to the next conception after the third sibling is 72 % lower compared with the interval after the first sibling; and the time to conception of a further sibling after the sixth child is 94 % lower with respect to the spacing between the first two siblings. These effects are significantly different from each other, as shown in Fig. 2, where we depict the coefficients for net parity with the relative confidence intervals estimated in columns 1 and 2 of Table 4. The figure clearly shows how not accounting for family heterogeneity conceals the positive impact of parity on the spacing of family births. We obtain these findings while accounting for age-related changes in maternal fecundity by controlling, in a time-varying fashion, for the age (and its square) of the mother during the interval. Interestingly, we find that after we account for family heterogeneity, the impact of child death on the successive birth interval increases in size. This finding suggests that unobserved heterogeneity at family level is correlated with child death and estimates not accounting for family heterogeneity provide biased estimates.
The impact of the real wage on the spacing of births remains highly significant also in the specifications including parity dummy variables. This leaves an important question: Does the effect of wages on births vary with parity? The underlying hypothesis here is that the decision to postpone a birth during hard times may be exacerbated by the presence of other dependent children. We test this hypothesis by interacting the real wage with the parity fixed effects. As shown in column 2 of Table 4, we stratify by family and quarter-century. Column 3 reports the results, establishing that not only are higher parities associated with significantly larger birth intervals but that the size of the demographic response to changing real wages also rises significantly with parity. The coefficients of the interactions show that the impact of real wages on spacing increases up to parity 3 (the interval between the third and fourth sibling) and then stabilizes. The coefficients for the interaction terms imply that if the real wage decreases by 1 standard deviation, the time to the next conception is approximately 8 % lower for the third child (parity 2) and 13 % lower for the fourth child (parity 3) compared with that of the second child (parity 1, the reference group).Footnote 17 The fact that the real-wage effect varies across parity seems to suggest that birth spacing was a deliberate decision rather than a biological mechanism.Footnote 18
It is also possible to quantify the effects of the real wage and of parities in terms of time. Consider the baseline estimate with parity fixed effects and stratification by family as in column 2 of Table 4. The birth interval associated with the first parity (first two siblings) is 493 days; the birth interval associated with parity 2 (siblings 2 and 3) is 599 days, for a difference of 106 days. This difference increases to 161 days if we consider the birth interval between siblings 3 and 4 with respect to the first interval in the family.Footnote 19 As for the real wage, an increase of the real wage by 1.5 standard deviations is associated with the postponement of a conception by about 54 days.Footnote 20
Note that the mechanical association between parity and the mother’s age at conception could affect the parity fixed-effect estimates. Moreover, for high parities, parity might be positively correlated with fecundity (Larsen and Vaupel 1993), which in turn would influence the length of the birth intervals affecting the size of our coefficients. To account for these factors, we reestimate in Table 5 our model with parity fixed effects for different age groups of mothers, constraining the sample to families that reach a maximum of five children. The rationale is that within a given age group, such as mothers aged 15–24, age-related fecundity is fairly constant, allowing us to estimate the “true” effect of parity on birth spacing. Moreover, by constraining the sample to families with a maximum of five children, we avoid the issue that high parities are independently correlated with fecundity and hence birth spacing.
Table 5 Parity-dependent birth spacing by mother’s age
The estimates shown in column 1 of Table 5 support our previous findings. Within each age group, growing parities are associated with longer birth intervals. Interestingly, we also find that the impact of the real wage on birth spacing is larger and highly significant among young mothers (column 1), suggesting that households responded more strongly to changes in economic conditions during early stages of their life, when they were presumably more financially unstable.Footnote 21
Our evidence of parity-dependent spacing is similar to that observed by Van Bavel (2004a) and others studying settings elsewhere in Europe during later periods: the larger the size of the families, the more the couples strive to postpone the next birth.